Make the Base Sugar Cookie Dough: Whisk the flour, baking powder, and salt in a bowl.
Beat the butter and sugar in a stand mixer fitted with the paddle attachment until fluffy and creamy, stopping the mixer and scraping down the sides midway if you have to, 3–4 minutes. Stop the mixer, then add the eggs and vanilla, return to medium speed and beat until creamy, 2 minutes. Stop the mixer, add the dry ingredients, then turn on the mixer to low and beat until everything is incorporated, being careful not to overwork the dough. Divide the dough into three equal-sized pieces. Wrap one third of the dough in plastic wrap and chill for one hour.
Preheat the oven to 350°F. Remove the dough from the fridge, unwrap, and divide the dough into 16 equal-sized pieces (like the size of small walnuts). Roll each piece into a ball, then arrange three inches apart on parchment-lined baking sheets and press with the center of your palm into a 2-inch round. Bake until lightly golden around the edges, 10–11 minutes. Cool completely. Store in an airtight container for up to 4 days.
Make the Icing and Decorate Cookies: Set up as many color bowls as you want by whisking 1 cup of confectioners’ sugar with 2 ½ tablespoons whole milk in a small bowl. Add liquid or powdered food coloring by the ¼ tablespoonful to reach the desired shade, adding tiny amounts of milk and teaspoons of confectioners’ sugar to reach a thick, but still pourable texture.
Pour ¼ cup of icing into a ramekin or small bowl, just a bit larger than the circumference of a cookie. Add 2 tablespoons of a second color on top of the first color. Gently press a cookie, top side down, into the colors, then lift the cookie out and let the excess drip. Using a toothpick, swirl a pattern between the two colors, if you’d like. You can also add a drop of food coloring directly to the cookie for a more vibrant color to swirl in; have fun with it! Arrange it, colored side up, on a parchment-lined baking sheet or plate, Repeat with remaining cookies and colored iced cookies, then let the icing firm up for about 1–1 ½ hours. Store in an airtight container for up to four days.