You will need sixty 1 3/4-by-3 3/4-inch molds to make the financiers.
In a small saucepan, melt butter over medium-high heat until nut-brown in color, about 6 minutes. Remove pan from heat and pour butter into a bowl, leaving any burnt sediment behind.
In the bowl of a mixer fitted with the paddle attachment, combine both flours, baking powder, sugar, and salt on low speed. Slowly add egg whites and beat for 2 minutes. Slowly add in browned butter on low speed; beat to combine, 3 minutes. Cover and refrigerate batter at least 2 hours.
Preheat oven to 375 degrees. Butter and flour molds. Fill three-fourths full with batter, and top with berries. Bake for 15 minutes or until lightly golden and firm to the touch. Serve warm.