Preheat oven to 425ºF and line a standard 12-cup muffin tin with paper liners.
Place butter in a small skillet set over medium-low to medium heat. Cook until the butter melts, foams up, and turns golden-brown, whisking occasionally. Remove from heat and cool briefly.
Add chocolate chips to browned butter to submerge and let sit for a few minutes. Whisk until smooth, and then whisk in vanilla extract. Set aside.
Meanwhile, in a food processor fitted with the steel blade attachment, pulse almond meal, sugar, cocoa powder, espresso powder, and salt together until evenly combined. Transfer to a large bowl.
In a separate bowl, beat egg whites until foamy. Add to dry ingredients and fold in until partially incorporated. Add chocolate mixture and fold in until completely incorporated and even in texture.
Divide batter evenly between the prepared muffin cups. Bake in preheated oven for 20-25 minutes, until a toothpick inserted into the center of one of the financiers comes out with just a few moist crumbs.
Cool briefly in pan, and then transfer to a wire rack to cool completely. Store in an airtight container at room temperature. If desired, dust with powdered sugar before serving.
*I used store-bought almond meal, but if you decide to grind your own, I’d suggest sifting it before measuring to make sure it’s nice and fine. This will give the financiers a better texture.