Step 1

Preheat oven to 350°F, and line 2 baking sheets with parchment paper. Stir together flour, cocoa, baking soda, and salt in a large bowl. Beat butter and brown sugar with a stand mixer fitted with a paddle attachment on medium speed until light and fluffy, about 3 minutes. Add eggs, 1 at a time, beating until blended after each addition. Add vanilla and 2 teaspoons food coloring gel, and beat until well blended, adding more food coloring, as needed, to reach desired shade.

Step 2

Add half of flour mixture, and beat on low speed until well blended. Add milk, and beat until blended. Add remaining flour mixture, and beat until blended. Fold in white chocolate chips using a rubber spatula. Refrigerate dough for 15 minutes.

Step 3

Place powdered sugar in a small bowl. Roll dough into 1-inch balls, and roll dough balls in powdered sugar. Place on prepared baking sheets, spacing 2 inches apart.

Step 4

Place 1 baking sheet of cookies in refrigerator until ready to bake. Bake remaining baking sheet of cookies in preheated oven until cookies are set in center and lightly browned on bottoms, about 16 to 18 minutes, rotating baking sheet from front to back halfway through bake time. Transfer cookies to a wire rack to cool completely, about 30 minutes. Meanwhile, repeat procedure with remaining baking sheet of cookies.