Brown the butter: Place the cubed butter in a small to medium-sized saucepan with a light-colored interior (so you can see the color change) over low to medium heat.
Swirl the pan until all the butter is melted. This also helps a bit with some of the sputtering (be careful!).
Once the butter is melted, continue to heat it on the stove. At first, there will be big bubbles, then this changes to smaller bubbles, and eventually it foams. Watch for the first signs of browning on the bottom of the pan. You may need to angle the pan to see this.
As soon as you see browning, remove the pan from the stove. The butter will continue to cook with the residual heat for the next several minutes. By turning off the heat at the first sign of browning, you'll prevent it from burning. Set aside to cool.
Into a large bowl, pour the almond flour, powdered sugar and flour. Whisk together and then whisk in the egg whites and vanilla. Mix well to get out any lumps.
Next, pour in the browned butter and carefully whisk into the batter. Then, stir the chopped chocolate into the batter (even the chocolate dust). Cover and let chill for at least 1 hour or up to 3 days, to firm up.
When you're ready to bake the tigré, preheat your oven to 350˚F (175˚C).
Spray a standard 12-well muffin (or mini doughnut pan) with baking spray or brush with melted butter.
Divide the batter equally among the wells, filling them one-quarter of the way full. Place a piece of parchment paper on top of the muffin tin, then top with a flat story baking sheet. This will encase the cakes during the baking process so you will have flat cakes, instead of domed.
Bake for 20 minutes, then remove the baking sheet and parchment paper. Bake for another 3 to 5 minutes, or until the sides are browned and pulling away from the sides. Remove from the oven, let cool for 5 minutes in the tin and then turn out onto a clean surface.
Use the back of a teaspoon-sized measuring spoon to firmly press into the bottom of each warm cake to make an indentation. Sometimes you need to try a second time for the indentation to stay. Be sure to do this while the cakes are still warm.