Step 1Combine the egg whites and sugar in a medium bowl. Place the bowl over a similar-sized saucepan to form a bain-marie or double-boiler filled with gently simmering water. Stir the egg whites and sugar with a whisk just until the whites warm slightly and the sugar dissolves. Remove from the heat and set aside.
Step 2In a small saucepan, cook the butter over medium heat until it begins to brown and gives off a nutty aroma. Remove from the heat to prevent the butter from overcooking. Set aside, but keep very warm.
Step 3In a large bowl using a hand mixer, or in the bowl of a stand mixer, begin whisking the egg white mixture at low speed. With the mixer running, gently add the flour, followed by the almond flour, and mix just to combine. Add in the warm butter in a thin stream, mixing at low speed until it is incorporated. Scrape the sides and bottom of the bowl, and continue to mix 10 seconds more to ensure the batter is completely combined. Cover and refrigerate for at least 1 hour, preferably overnight.
Step 4Heat the oven to 325 degrees. Spray or butter a tray of miniature muffin molds (our molds measured 1 3/4 -inch wide by one-half-inch deep). Fill the molds two-thirds full with batter, and place a fresh raspberry on top of each. Place the tray in the oven and bake 30 to 40 minutes, until golden. Remove and cool on a wire rack. Repeat with the remaining batter.