Preheat oven to 350°F. Line 2 baking sheets with parchment paper or silpats. Set aside In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
1 ¾ cups all-purpose flour, ½ teaspoon baking powder, ¼ teaspoon baking soda, ¼ teaspoon kosher salt
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and sugar together on medium-high speed until smooth and creamy, about 2 minutes.
10 tablespoon unsalted butter, 1 cup granulated sugar
Add the egg and vanilla, beating on high speed until thoroughly combined, about 1 minute. Scrape down the sides and bottom of the bowl and beat again to ensure ingredients are evenly combined.
1 large egg, 2 teaspoons vanilla extract
Reduce to low speed and add the dry ingredients in 3 additions, alternating with the sour cream. Beat everything on low until combined and no pockets of flour remain. Batter will be thick.
⅓ cup full-fat sour cream
Using a large ¼ cup cookie scoop, drop dough 4 inches apart onto prepared baking sheets, 6 cookies per sheet. Bake for 16-18 minutes or until the edges are lightly browned. Allow cookies to cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely before icing. Whisk the powdered sugar, milk, corn syrup, vanilla, and salt together in a medium bowl.
5 ½ cups powdered sugar, 6 tablespoons whole milk, 2 tablespoons light corn syrup, 1 teaspoon vanilla extract, ½ teaspoon kosher salt
Divide icing evenly between 4 bowls. Using gel food coloring, dye each bowl of icing into following colors: yellow, purple, pink, and green.
red, blue, yellow gel food coloring
On the flat side of each cookie, spread one color icing onto one half of each of the cookies. Refrigerate for 15 minutes or until set so that the icings do not bleed into each other. Spread another color icing onto other half of the flat side of the cookies and allow the icing to set completely, about 1 hour, before serving.