Preheat to 350℉ (175℃). Grease a 9-inch round pan or a 9-inch square pan.: As the oven warms you will notice a faint warm air shift, and the preheated environment ensures the cake begins to rise immediately on contact with heat. Proper greasing prevents sticking and encourages even browning around the edges. A common mistake is underheating the oven, which slows rise and creates a dense crumb, so use an oven thermometer if yours runs cold or hot.
Cream the 3/4 cup butter with the 3/4 cup sugar until fluffy. Mix in the salt and vanilla. Add the egg yolks to the sugar mixture and beat until creamy.: When creaming, you should see the mixture lighten in color and take on a slightly airy texture, the butter smelling rich and the sugar fine against the paddle. After adding the yolks , the batter becomes silkier and more cohesive, and the aroma of vanilla extract will bloom. If you skip sufficient creaming you lose trapped air, resulting in less lift, so be patient until you have a fluffy base.
Combine 2 1/4 cups flour with the baking powder; add the flour mixture and the milk to egg yolk mixture and mix until well combined.: The dry ingredients should be whisked so the baking powder is evenly distributed, then added alternately with milk to maintain a smooth batter. Look for a cohesive, slightly thick batter that holds a soft ribbon when lifted. Overmixing at this stage will develop gluten and yield a tougher cake, so stop when dry streaks disappear.
Coat berries with 1 1/2 tablespoons flour and fold into the batter.: Tossing the blueberries in a light dusting of flour keeps them suspended as they bake, and folding them gently prevents bruising. Visually you want a batter dotted with evenly coated berries, without purple streaks. If you stir too vigorously the berries will burst and bleed, turning the batter purple and creating dense wet pockets.
In a separate bowl, beat the egg whites until soft peaks form. Add 1/3 cup of the sugar, 1 tablespoon at a time, and beat until stiff peaks form. Fold the egg whites into batter. Pour into the prepared pan. Sprinkle top with remaining 1 1/2 tablespoons sugar.: The whipped egg whites should look glossy and airy, and as you add the sugar they stabilize into firm peaks that hold shape. Folding them in preserves the trapped air, which is why the cake gains its delicate lift. Pouring into the pan you'll hear a soft thud as batter settles, and sprinkling extra sugar on top gives you that crisp, sugary crust. A frequent error is overfolding, which deflates the whites and yields a heavy texture.
Bake for 50 minutes, or until cake tests done.: As the cake bakes you will smell a deepening butter and vanilla scent, and the top will turn a warm golden color with edges pulling slightly from the pan. A toothpick inserted into the center should come out with a few moist crumbs, not wet batter, indicating doneness. Opening the oven door repeatedly will drop the temperature and can cause sinking, so resist peeking often.
Let the cake cool in the pan for 5 minutes then transfer it to a cooling rack to finish cooling. Dust with icing sugar if preferred and serve.: Resting briefly in the pan allows the crumb to set while still warm, and transferring to a rack prevents residual heat from steaming the base. Cooling releases the full aroma and firms the texture so slices hold cleanly. If you cut too soon the cake may crumble, which is the usual misstep here, so allow those few cooling minutes before slicing and serving.