Best Ever Chai Cookies

Name: Best Ever Chai Cookies
Prep time: 10 min
Cook time: 10 min
Total time: 20 min
Cuisine: American
Ingredients: 2 1/2 cups all-purpose flour; 1 1/2 cups cake flour; 2 tsp. cornstarch; 1 tsp. baking soda; 1 tsp. baking powder; 1 tsp. salt; 2 Tbsp. chai spice blend, divided (recipe below); 16 Tbsp. unsalted butter, cold, cubed (1 cup butter); 1 cup sugar (+ 1 Tbsp. for rolling); 1/4 cup brown sugar, packed (light or dark); 2 large eggs; 2 large egg yolks; 2 tsp. vanilla extract; 2 tsp. ground cinnamon; 1 tsp. ground ginger; 1 tsp. cardamom; 1/2 tsp. allspice; 1/2 tsp nutmeg; 1/2 tsp. cloves; 1 1/2 cups confectioners' sugar; 3 Tbsp. milk (plus more as needed); 1 tsp. vanilla bean paste