Preheat the oven to 400°F (204°C). Butter and flour 2 mini-muffin tins.
In a large bowl, sift together the all-purpose flour and salt. Add the almond flour, granulated sugar, and confectioners sugar and whisk well to combine.
In another bowl, whisk the almond extract into the egg whites just until frothy, 30 to 60 seconds.
In a wide saucepan over low heat, melt the butter. Then bring the heat up to medium and let simmer, without stirring, for 5 to 10 minutes, until the milk solids have sunk to the bottom and have begun to turn light brown. You will hear the butter gurgle and snap as it cooks and begins to turn amber. Watch it carefully as you don't want it to turn too dark a shade of brown. You may want to cover the pan with a lid or a spatter screen to prevent little droplets of hot butter landing on you or your stovetop. When the butter turns an amber color, remove the pan from the heat. You just made brown butter.
Add the dry ingredients to the egg white mixture and gently whisk until combined. While the butter is still hot, pour it through a fine mesh strainer into a bowl or measuring cup. You should have just shy of 1/2cup. Pour this into the batter and gently whisk just until the butter is incorporated and the batter is smooth.
Pour the batter into the mini-muffin pans, filling them to the top. Reduce the oven temperature to 375°F (190°C) and bake the financiers for 13 to 15 minutes, until they have risen in the center and the edges are golden brown.
Cool the financiers in the pans for at least 10 minutes and then turn them onto a wire rack to cool completely. The financiers are quite delicate, especially when warm, so if they stick to the pan, simply run the blade of a thin knife around the edge of each financier prior to turning them out of the pan. If desired, lightly dust the tops with confectioners sugar.