Cream sugar and butter together in a large bowl of a stand mixer afixed with an S blade or with a hand mixer. Mix until pale yellow, fluffy, and well-incorporated.: The bowl should sound slightly hollow as the mixer runs and the mixture will lighten in color and texture, becoming pale and airy; this trapped air is what gives the cookies lift. You'll feel a silky, smooth texture under the paddle and see tiny ribbons when you lift it up, those ribbons dissolve back in slowly. If the mixture looks gritty, scrape the bowl and continue briefly until smooth. A common mistake is using butter that is too soft, which yields a greasy mixture, so aim for butter that dents with slight pressure but holds shape. The aroma at this stage is light and buttery, with a faint sweetness as the granulated sugar begins to dissolve.
Add the egg yolks and lemon zest and mix until well-combined.: Right after adding the egg yolks and the fragrant oils from the lemon zest , the mixture gains a richer sheen and a subtle citrus perfume will bloom, signaling aromatic balance. Mixing should be gentle and just long enough to incorporate everything uniformly; overmixing at this point can lead to a tougher final cookie because the yolks increase emulsion. Watch for a homogenous batter where no streaks of yolk remain. A trap to avoid is tossing in the zest with high-speed mixing because that can spread bitter pith if present, so add zest and mix on low until combined.
Sift the flour over the wet ingredients, and mix just until combined.: As you add the sifted all purpose flour , you'll notice the mixture transitioning from glossy to a more doughlike consistency. The sound changes from slapping to a soft thud as the flour absorbs moisture. Mix briefly, using a folding motion if working by hand, until you no longer see dry streaks of flour. This short mixing period helps preserve tenderness. Overworking here is the usual misstep, and it causes gluten development, which tightens texture, so stop as soon as combined.
Knead together very gently until it forms enough of a ball to plop onto a piece of plastic wrap. Work the dough just enough to get it to stick together, but be careful not to overdo it. Honestly, I get so paranoid about overworking the dough that I pile the crumbs onto the plastic wrap, fold it up around the mound, and press it together that way.: The tactile cue you want is a cohesive, slightly tacky dough that holds when pressed, not a smooth elastic mass. When pressing in the plastic wrap method, you minimize handling and heat transfer from your hands, which helps keep the butter firm. If you squeeze too hard or knead extensively, the cookies may become dense and lose flakiness. The dough will feel cool and slightly crumbly until it binds, and that's normal; patience at this stage preserves tender crumb.
Completely wrap the dough with the plastic wrap and chill the dough for at least three hours.: Chilling firms the butter so the shapes stay crisp in the oven, and it lets the flour hydrate for a cohesive texture. During this time the flavors meld and the dough becomes much easier to roll. I mark the time and place the wrapped dough on a flat tray so it chills evenly. If you try to roll warm dough, it will stick and spread; if you skip chilling altogether, the shapes will flatten in the oven, which is the most common error.
When you're ready to pull the dough out and prepare it, preheat oven to 350°F (175°C).: Preheating the oven ensures that the cookies begin baking immediately, creating a quick edge set that preserves shape and yields that light, tender interior. You'll hear a faint settling sound as the oven reaches temperature, and the heating element glow will stabilize. I always give the oven a few minutes after reaching target to ensure consistent heat. Failing to preheat can lead to uneven texture and longer bake times, so set the oven before rolling.
Roll out dough – I go as thin as 1/8 inch, but I prefer about 1/4 inch thick. Cut into shapes, adding additional flour as necessary to avoid sticking. Place cookie shapes on a cookie sheet (no need to grease).: When rolling, the dough surface should feel cool and slightly floured but not dry. A 1/4 inch thickness gives a tender, slightly substantial bite while 1/8 inch will be crisper; choose based on preference. Press cutters straight down and lift cleanly to avoid dragging the dough. Lightly flour both the surface and the cutters to prevent sticking, and transfer shapes with a thin metal spatula if they feel fragile. Overflouring can toughen edges, so use sparingly.
Bake just until the cookies start to turn pinky beige around the edges, around 8 minutes. Let cool for a couple of minutes on the baking sheet, then move to wire rack to cool completely.: Visually the cookies will go from pale to a gentle pinky beige at the rims, and the centers will no longer look wet. The aroma shifts to a slightly caramelized butter scent. Letting them rest briefly on the sheet helps them set so they do not split when moved. A common error is overbaking, which yields dry, hard cookies, so watch closely during the last minute.
To make the icing, add the powdered sugar, 2 tablespoons milk, corn syrup, and the vanilla to a small mixing bowl. Use a wire whisk or a fork to mix it well. If it's too thick, add more milk a teaspoon at a time. You want the icing to be thin enough to be pipeable but thick enough to hold a line. Transfer the icing into a piping bag with tip or a Ziploc bag with the end snipped off, and pipe the icing onto the cookies. Let the icing sit until it hardens before storing or assembling on cookie plates.: The icing should be glossy and smooth, and when you dip a spoon in and lift, it should fall back in thick ribbons that level out. The corn syrup gives that sheen and prevents graininess. Adjust the milk a teaspoon at a time for control. When piping, steady pressure and a light wrist make clean lines. If you rush the piping, the icing can flood into unintended areas, so practice on a spare cookie first.
Cookies keep up to one week in an airtight container.: When stored at room temperature in a sealed container, the cookies retain texture and the icing remains set. Layer them with parchment to avoid sticking, and keep away from direct sunlight or heat which can soften the icing. A typical mistake is stacking warm cookies, which traps steam and makes them limp, so always cool completely first.