Preheat oven to 350°F (175°C). Brush the cavities of a mini muffin pan with melted butter and dust with flour. Remove any excess flour and refrigerate the mold.
To make the brown butter, in a small saucepan, heat butter on low to medium heat, occasionally swirling the pan over the stovetop for about 5-10 minutes.
It will foam at first, but then it will begin to brown, producing dark golden flecks (browned milk solids). Check the color and once you are happy with the level of browning, pour the butter (with milk solids) into a bowl to stop cooking. Let it stand and fully cool down.
To make the cake batter, using an electric mixer whisk egg whites for 15-20 seconds and set aside. In a separate bowl, combine sugar, all-purpose flour, almond, and hazelnut flour. Add beaten egg whites to the dry ingredients and mix with a hand whisk. Stir in the brown butter.
Pour the batter into the mold filling the holes up to two-thirds. Bake for 15 to 20 minutes, until golden brown. Check financiers with a toothpick: if it comes out dry, they are ready. Remove from the oven, and let cakes cool for 2-3 minutes before removing them from the mold. Serve warm or at room temperature.