Sift flour and salt together through a fine-mesh strainer into a small bowl; set aside.
In the bowl of a food processor fitted with a blade attachment, process the almonds until finely ground, about 1 minute.
Add sugar and pulse until well combined, about 10 (1-second) pulses.
Transfer mixture to a large bowl; set aside.
Melt butter in a medium frying pan over medium-low heat, swirling the pan occasionally until butter turns amber in color and smells nutty, about 15 minutes.
Strain through a fine-mesh strainer into a medium heatproof bowl, add vanilla seeds and pod, and stir to break up any clumps of vanilla seeds.
Place egg whites in a medium bowl and whisk until frothy, about 30 seconds.
Stir egg whites into reserved almond mixture with a rubber spatula until just combined.
Fold in reserved flour mixture until just combined (do not overmix).
Remove vanilla pod from butter and discard.
Gently stir butter into flour mixture, a little at a time, until butter is absorbed and just evenly combined (do not overmix).
Cover batter with plastic wrap and refrigerate for 1 hour.
Meanwhile, heat the oven to 450 degrees F and arrange a rack in the middle.
Generously coat a 24-well mini-muffin pan with butter and place on a baking sheet.
Fill each muffin well completely with batter and bake for 6 minutes.
Reduce heat to 400 degrees F and bake financiers until just beginning to brown around the edges, about 8 to 10 minutes more.
Immediately unmold financiers and cool completely on a wire rack.