Biscuits and Chocolate Gravy

Name: Biscuits and Chocolate Gravy
Ingredients: 1 stick unsalted butter, cut into small cubes; 2 1/2 cups all-purpose flour, plus more for dusting; 2 tablespoons baking powder; 1 tablespoon sugar, plus more for sprinkling; 1 3/4 teaspoons kosher salt; 1 cup cold whole milk, plus more for brushing; 2 cups whole milk; 3/4 cup sugar; 1/3 cup natural cocoa powder (not Dutch-process); 3 tablespoons all-purpose flour; 2 tablespoons cold unsalted butter, cut into pieces; 1 1/2 teaspoons pure vanilla extract