Baked Cake Donuts

Name: Baked Cake Donuts
Ingredients: ½ cup (1 stick) unsalted butter, room temperature, plus more for pans; 2 ½ cups unbleached all-purpose flour; 1 ½ teaspoons baking powder; ¼ teaspoon baking soda; ⅛ teaspoon freshly grated nutmeg; ¾ teaspoon kosher salt; ½ cup granulated sugar; ¼ cup light brown sugar; 2 eggs, room temperature; 1 teaspoon pure vanilla extract; 1 cup whole milk, room temperature