Black and White Cookies

Name: Black and White Cookies
Ingredients: 1 3/4 cups ( 210 g ) all-purpose flour; 1/4 cup ( 28 g ) cornstarch; 1/2 teaspoon baking powder; 1/4 teaspoon baking soda; 1/2 teaspoon salt; 10 tablespoons ( 140 g ) unsalted butter , room temperature; 1 cup ( 200 g ) granulated sugar; 2 large eggs; 1/2 cup ( 113 g ) sour cream; 2 teaspoons vanilla extract; 1 lemon , zested , optional; 3 cups ( 340 g ) powdered sugar; 6 tablespoons whole milk , divided; 1 teaspoon vanilla extract; 1/4 cup ( 21 g ) unsweetened Dutch-processed cocoa powder; Offset spatula