EASTER EGG SUGAR COOKIES

Steps:

• For the sugar dough: Whisk together the flour, salt and baking soda in a medium bowl. Beat together the vanilla and egg in a small bowl.
• Beat the butter, granulated sugar and confectioners' sugar together in a large bowl with an electric mixer on low speed. Once incorporated, increase the speed to medium and beat until slightly creamy, about 3 minutes. Stop and scrape down the sides of the bowl using a rubber spatula as needed.
• Reduce the speed to low again, slowly pour in the egg mixture and beat until combined. Add the flour mixture in 3 additions, beating until combined after each and increasing the speed as the dough gets thicker to keep the beaters spinning. Scrape down the sides of the bowl and the beaters as needed. Once all the flour is just incorporated, increase the speed to medium-high and beat until the dough is very smooth, about 5 minutes.
• Turn the dough out of the bowl and bring it together. Divide into 2 even pieces. Shape each piece into a flat square and wrap in plastic wrap. Refrigerate the dough for at least 3 hours or overnight.
• Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment.
• Dust another sheet of parchment with flour and put 1 dough piece on top. Dust with more flour and top with another sheet of parchment. Roll the dough out between the parchment sheets into a square about 1/4 inch thick (and about 11 by 9 inches) and place in the freezer for 5 minutes. Repeat with the remaining piece of dough.
• Working with 1 dough sheet at a time, cut out cookies with a 2 1/2- by 2 2/4-inch Easter egg cookie cutter and arrange on the prepared baking sheets, about 2 inches apart. Refrigerate while you cut the remaining cookies. Reroll any scraps of dough and repeat the freezing, cutting and refrigerating process until all the dough is used. Repeat with the remaining dough sheet.
• Bake, rotating the baking sheets front to back and bottom to top about halfway through, until cookies are golden brown around the edges, about 12 minutes. Let cool completely on the baking sheets set on a wire rack, about 30 minutes.
• For the icing: Meanwhile, sift the confectioners' sugar into a large bowl. Add milk, 1 tablespoon at a time, whisking until the icing is thick enough to show the line of the whisk that disappears within about 8 seconds.
• Place 3 tablespoons white icing in each of 3 separate bowls. Tint each a different color and cover with plastic wrap (see Cook's Note). Place 1/4 cup white icing in another bowl, covering the remaining white icing with plastic wrap so it does not dry out. Drizzle one of the colored icings (about 1 tablespoon) onto the 1/4 cup white icing and swirl with a toothpick.
• Next, dip the surface of a cookie in the swirled icing and remove slowly, allowing any excess to drip off. Shake the cookie over the bowl of icing to remove any excess. Gently smooth the icing with a toothpick to fill in any gaps, if necessary. Place the finished cookies on a wire rack over a baking sheet. Use the tip of the toothpick to pop any bubbles that appear. Drizzle more colored icing as needed. Repeat this process with the next 2 colors and the remaining white icing until all the cookies are decorated. Let set for 30 minutes. Store single layers of cookies, with parchment in between, in a tightly sealed container for up to 1 week.