In a saucepan over medium heat, melt the butter. Continue to cook it, swirling occasionally, until it turns a nutty brown color and has a toasted aroma. This usually takes about 5-7 minutes. Be careful not to burn it! Once browned, pour the butter into a heatproof bowl and let it cool slightly.
In a medium bowl, whisk together the almond flour, powdered sugar, all-purpose flour, baking powder, and salt. This ensures that the baking powder is evenly distributed for a good rise.
Add the slightly cooled browned butter to the dry ingredients. Stir until just combined. Don't overmix!
In a separate bowl, lightly whisk the egg whites until they are slightly frothy. Add them to the butter mixture along with the almond extract. Stir until everything is well combined.
Gently fold in the finely chopped pistachios into the batter. Make sure they are evenly distributed throughout.
Preheat your oven to 375°F (190°C). Grease a financier pan (or a muffin tin) very well with butter or cooking spray. Pour the batter into the molds, filling each about 3/4 full.
Bake for 15-18 minutes, or until the edges are golden brown and a toothpick inserted into the center comes out clean.
Let the Pistachio Financiers cool in the pan for a few minutes before carefully removing them to a wire rack to cool completely.