Brown the Butter: Melt the unsalted butter in a medium-sized saucepan. As it cooks, the butter will foam and orangey-brown bits will begin forming along the bottom of the pan. This process takes about 5 minutes.
Cool the Butter: Remove the saucepan from the heat and allow the browned butter to cool before adding it to the batter.
Prepare the Oven: Preheat the oven to 350°F (175°C). Spray the donut pan thoroughly with non-stick spray and set it aside.
Combine the Dry Ingredients: In a medium-sized bowl, whisk together the all-purpose flour, packed light brown sugar, salt, and baking powder until evenly combined.
Mix the Wet Ingredients: In a separate bowl, combine the cooled browned butter with the full-fat sour cream and egg, mixing them together.
Form the Batter: Gently fold the wet mixture into the dry ingredients until the batter is combined, taking care not to overwork it.
Fill the Donut Pan: Spoon the prepared batter into the greased donut pan, distributing it among the donut molds.
Bake the Donuts: Place the filled pan in the preheated 350°F (175°C) oven and bake for 20–25 minutes, or until the donuts spring back when lightly pressed.
Cool in the Pan: Remove the baked donuts from the oven and let them cool in the pan for 10 minutes.
Finish Cooling: Remove the donuts from the pan and allow them to cool completely before adding the glaze.
Prepare the Glaze: In a small bowl, whisk together the powdered sugar, vanilla extract, and milk until the mixture is smooth and free of lumps.
Adjust the Glaze: If the glaze is too thick, add more milk until it reaches a suitable consistency for dipping.
Glaze the Donuts: Dip the tops of the completely cooled donuts into the vanilla glaze, allowing the glaze to coat the surface.
