Step 1

For the sugar dough: Whisk together the flour, baking soda and salt in a medium bowl. Beat together the egg and vanilla in a small bowl.

Step 2

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 as needed.

Step 3

Reduce the speed to low again and slowly pour in the egg mixture and beat until combined. Add the flour mixture in 3 additions, 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.

Step 4

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.

Step 5

To roll, cut and bake the cookies: Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment paper.

Step 6

Dust another sheet of parchment paper with flour and put 1 piece of the dough 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 (about 11-by-9 inches) and place in the freezer for 5 minutes. Repeat with the remaining piece of dough.

Step 7

From 1 piece of rolled dough, cut out cookies with a 2 1/2-inch 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.

Step 8

Bake, rotating the baking sheets front to back and bottom to top about halfway through, until golden brown around the edges, about 12 minutes. Let cool completely on the baking sheets set on a wire cooling rack, about 30 minutes.

Step 9

Meanwhile, make the royal icing: Combine the confectioners' sugar and meringue powder in a large bowl. Add 3 tablespoons water and the vanilla and beat with an electric mixer on medium-high speed until the icing forms thick and glossy peaks, about 2 minutes (add up to 1 tablespoon more water, if needed). Tint with a few drops of food coloring if desired.

Step 10

Fit a pastry bag with a small round tip and fill it with the icing.

Step 11

Pipe royal icing on cookies with the design of your liking and let dry for 30 minutes.