Place the butter in a small saucepan over medium-low heat. Let it melt slowly, then increase the heat to medium and continue cooking. Stir gently with a heatproof spatula as the butter bubbles and pops. Once the bubbling calms down, tiny golden specks will appear at the bottom of the pan, releasing a warm, nutty fragrance. Once the butter turns golden yellow with chestnut-colored solids, remove it from the heat and transfer to a heatproof bowl to cool slightly.

Place the toasted almonds and flour into a food processor or blender and pulse until combined. Pulse until the mixture resembles fine, sandy crumbs. Transfer this to a large mixing bowl.

Blend the powdered sugar and salt into the almond-flour base, whisking until smooth and uniform. Pour in the egg whites and whisk until you have a smooth, pancake-like batter with no dry spots. Slowly drizzle in half of the browned butter, whisking until fully incorporated, then add the remaining butter and whisk again until smooth. Cover the bowl with plastic wrap and refrigerate for at least 3 hours or up to overnight.

Preheat your oven to 375°F (190°C) and lightly grease a 24-cup nonstick mini muffin pan. After the batter has rested in the fridge, spoon roughly 1 tablespoon into each prepared muffin cup. Garnish each scoop of batter with sliced almonds before baking.

Bake for about 12 minutes, or until the cakes are puffed, lightly golden in the center, and deeper golden around the edges. Let the cakes rest in the pan for 10 minutes, then gently release them with a small spatula or butter knife. Serve warm or at room temperature.