Brown Butter Pumpkin Donuts

Name: Brown Butter Pumpkin Donuts
Prep time: 25 min
Cook time: 10 min
Total time: 35 min
Cuisine: American
Ingredients: 1/2 cup unsalted brown butter (melted); 1/2 cup granulated sugar; 1/2 cup light brown sugar; 2 large eggs (room temperature); 1 teaspoon vanilla extract; 1/2 cup pumpkin puree; 2 cups cake flour (substitute all purpose flour); 1 1/2 teaspoons baking powder; 1/4 teaspoon baking soda; 2 teaspoons pumpkin pie spice; 1/2 teaspoon kosher salt; 1/4 cup whole milk; 1 cup powdered sugar; 1 tablespoon unsalted brown butter (melted); 1/2 teaspoon vanilla; 1-2 teaspoons milk