Place the butter in a small saucepan. Melt over medium heat. Continue cooking until butter is boiling and turns golden brown and smells nutty, about 8 minutes. Pour into a bowl and cool for 30 minutes.
Preheat the oven to 175C. Grease the wells of a mini muffin pan by brushing them lightly with softened butter.
In a large mixing bowl, whisk together the powdered sugar, almond flour, all-purpose flour, and salt. Add the egg whites, vanilla, and cooled browned butter. Whisk together until just combined. (The batter will be thick.)
Divide the batter among the greased muffin pan cups. (I like to place the batter in a piping bag for easy filling!) They will be about three-quarters.
Bake for 15 to 20 minutes or until the edges are golden brown and a toothpick inserted into the center comes out clean. Let cool in the pan for 10 minutes. Remove and cool completely on a wire rack.