Melt the butter in a small skillet over medium-low heat. The butter will begin to foam; once the foam subsides, about 3 minutes, the milk solids will separate and fall to the bottom of the skillet. Continue to cook, swirling the skillet occasionally, until the milk solids turn a medium brown color and the butter has a nutty aroma, 2 to 3 minutes more; watch carefully as it can go from brown to burnt very quickly. Immediately remove the pan from the heat; the butter will continue to brown off the heat. Stir in the vanilla and almond extracts and set aside to cool completely, 10 to 15 minutes.

Whisk the confectioners' sugar, almond flour, cake flour and salt together in a large bowl. Whisk in the egg whites until smooth. Whisk in the browned butter until just combined. Let the batter rest, covered, in the refrigerator for 2 hours.

Preheat the oven to 375 degrees F. Spray a nonstick financier pan or mini muffin pan well with cooking spray.

Spoon the batter into a piping bag fitted with a large plain tip and pipe about half of the batter into the molds. Refrigerate the other half while the first batch bakes. Bake until puffed and set in the center with golden brown edges, 9 to 10 minutes if you’re using a financier pan or a few minutes more in a mini muffin pan.

Cool the pan on a rack for 2 minutes, then unmold the cakes and cool them on the rack completely. Wipe the pan clean and repeat with the remaining batter. These are best eaten the day they’re made.