Gather all ingredients.

Preheat the oven to 350 degrees F (175 degrees C). Line 2 large rimmed baking sheets with parchment paper; set aside.

For cookies, whisk flour, cornstarch, baking powder, salt, and baking soda in a bowl until no lumps remain; set aside.

Beat butter and sugar with an electric mixer in a large bowl on medium-high speed until light and fluffy, 2 to 3 minutes, stopping to scrape down sides of bowl as needed.

Add eggs, sour cream, and vanilla, and beat on medium-low speed until just combined, about 1 minute. The mixture will look curdled. Reduce speed to low and gradually add flour mixture, until fully incorporated, about 2 minutes, stopping to scrape down sides as needed. Cover and chill dough until firm and no longer sticky to the touch, at least 1 1/2 hours or up to 3 days.

Scoop dough with a 1 1/3 ounce scoop (#24, about 2 1/2 tablespoons) and place on the prepared baking sheets, spacing about 2 inches apart, 12 per baking sheet.

Bake in the preheated oven, one baking sheet at a time, until bottoms are golden brown and center is set, 14 to 16 minutes, rotating baking sheets front to back halfway through.

Using the back side of a spatula, lightly press tops down to create a flat surface. Transfer to a wire rack, and let cool to room temperature, about 30 minutes.

For frosting, beat butter in a bowl with an electric mixer on medium speed until smooth and creamy, about 2 minutes, stopping to scrape down sides of bowl as needed. Reduce mixer speed to lowest setting, and gradually add powdered sugar to butter, beating until just combined after each addition and stopping to scrape down sides of bowl as needed.

Add vanilla, salt, and food coloring, and beat on medium speed until smooth and fluffy, and food coloring is evenly combined, about 1 minute.