In a medium-size bowl, add the warm water, sugar, and yeast and whisk well to combine. Sit aside for about 10 minutes, or until the mixture has bubbled up and become foamy.: The first thing you'll notice is the aroma of yeast as the warm water wakes it up and the surface becomes frothy, signaling active fermentation. This foaming should be lively but not overly violent, and it often smells slightly yeasty and sweet; that scent reassures you the starter is healthy. The why here is simple, the yeast needs time to metabolize sugar and produce gas that will leaven the dough. One common mistake is using water that is too hot, which can kill the yeast and leave you with no rise. If you see no bubbles, it's safer to discard and start over with fresh yeast rather than push the recipe and end up with dense beignets. Keep the bowl in a warm spot, not in direct sun, to avoid overheating.
In the bowl of a stand mixer fitted with the paddle attachment, beat the eggs until smooth. Beat in the vanilla and evaporated milk. Beat in 3 and 1/2 cups of the flour until smooth. Turn the mixer to low speed and slowly pour in the yeast mixture (careful here - this mixture can splash up if added too quickly!); beat until smooth. Add in the butter and beat until incorporated. Finally, beat in the remaining 3 and 1/2 cups of flour and salt. Beat until dough is smooth and cohesive; about 2 minutes. Cover the bowl tightly with plastic wrap and refrigerate the dough for at least 2 hours, or up to 24 hours.: As you mix, the bowl will fill with a rich, creamy batter that gradually transforms into a cohesive dough. The smell will become buttery and slightly sweet from the evaporated milk and butter , and you may see the dough pulling cleanly from the sides of the bowl when the gluten develops properly. The slow addition of the yeast mixture keeps the batter from splashing and ensures even hydration. The refrigeration step chills the dough, firms the fats, and lets flavors meld while improving handling. A classic pitfall here is overflouring the dough and ending up dry; trust the texture and stop adding flour when the dough is smooth and slightly tacky. Another issue is undermixing which can leave the dough lumpy and uneven in structure, so aim for that cohesive, slightly elastic texture this stage promises.
Line a large rimmed baking sheet with three layers of paper towels, set aside.: Preparing the draining station in advance keeps the frying workflow tidy and the beignets crisp. The paper towels help absorb excess oil immediately, preventing pooling that can make the exterior soggy. You'll see the oil bead on the surface of the paper towel at first, then the beignets will rest on a slightly drier layer, which maintains crispness. Forgetting this step often results in greasy beignets, which detracts from their lightness. I recommend stacking a couple of towels and replacing them if they become saturated during a long fry session.
In a large enameled cast-iron pan, heat 4 inches of oil to 360 degrees (F). Remove the dough from the refrigerator. On a lightly floured surface, roll the dough out into a 1/4-inch thick rectangle. Cut the dough into 2 and 1/2-inch squares.: As the oil approaches temperature you will see a faint shimmer and possibly a thin wispy smoke, a sign that the oil is hot enough to create immediate steam and puff the dough. Working chilled dough helps it hold its shape when transferred to hot oil. Roll gently so the dough stays airy, and use a bench scraper or sharp cutter to make clean edges. Visual cues that you're ready include a smooth dough surface and a steady oil thermometer reading of 360 degrees F . A frequent error is rolling the dough too thin which yields flatter beignets, or too thick which prevents even frying. Keep the thickness consistent for uniform cooking.
In batches, fry the dough until they puff up and are golden brown in color, about 1 minute. Using a slotted spoon, transfer the beignets to the prepared baking sheet and repeat with remaining dough.: When each piece hits the oil it should sink slightly then pop back up as steam inflates the interior; the sound is a gentle sizzle that becomes a brisker crackle as the outer surface browns. Look for an even golden brown, not scorched spots, turning if necessary for uniform color. Frying in small batches preserves the oil temperature so each beignet puffs properly; overcrowding drops the oil heat and yields oily, heavy dough. Use a slotted spoon to lift them and let extra oil drain before resting on the paper towels. If the beignets absorb too much oil, it usually means the oil was not hot enough; adjust the heat and test with a small piece first.
Fill a piping bag (fitted with a small tip) with the lemon curd.: The curd should feel smooth and glossy, with a slightly thick, spoonable consistency that flows gently through the piping tip. When you squeeze, you should feel a slight resistance, and the curd should hold its shape before piping. The reason for piping is control, so you can deposit the right amount without tearing the beignet. If the curd is too warm it will be too runny and may leak, so cool it to room temperature before piping to avoid spills.
Using the end of a small spoon (or your finger) make a small hole in the side of each beignet. Insert the tip into each hole and fill until the center puffs up a bit (or the curd begins to spill back out the hole).: As you pipe, you will see the beignet gently inflate where the curd enters, a pleasant visual cue that the filling is reaching the interior. The curd should stop filling just as the dough puffs to avoid overfilling and rupture. A common slip up is making too large a hole which causes the filling to escape, or piping too vigorously which can split the beignet. Aim for a small entry point and steady pressure, and wipe the tip between beignets to keep presentation neat.
Dust with powdered sugar, top with berries, and serve at once!: The final moment is aromatic and tactile, the feather light dusting of confectioners' sugar melting slightly on the warm surface and the fresh berries adding contrast and color. You'll notice a gentle mingling of fried dough scent, citrus perfume, and berry brightness. Serve immediately for the best texture and flavor; letting them sit too long results in softer exteriors and a less vibrant contrast between curd and berries. If you need to hold them briefly, keep them in a single layer at room temperature to avoid sogginess.