Preheat. Set the oven to 390°F (200°C).
Brown the butter. Melt the butter in a saucepan over medium heat, stirring occasionally, until it turns golden brown and smells nutty — about 5–10 minutes. Transfer to a bowl and cool quickly by setting it in cold water.
8 tbsp unsalted butter
Mix egg whites and sugar. Whisk the egg whites and sugar together just until a little foam forms on the surface. You're not whipping them — just combining.
5 egg whites, 7 tbsp sugar
Add honey and vanilla. Stir in the honey and vanilla until incorporated.
1⅓ tbsp honey, ½ tsp vanilla extract
Add dry ingredients. Sift the almond flour, cake flour, cocoa powder, and baking powder together, then mix into the wet ingredients until smooth.
¾ cup almond flour, 7 tbsp cake flour, 3 tbsp cocoa powder, ½ tsp baking powder
Add the brown butter. Pour in the cooled brown butter, including the browned bits at the bottom — they carry a lot of flavor. Make sure it isn't too hot or it may cook the egg whites.
Prepare the pan. Line the bottom of an 8-inch pan with parchment. Grease the sides with butter and dust with powdered sugar for easy release.
powdered sugar
Bake. Pour in the batter — it will be fairly fluid. Place in the oven and immediately reduce the heat to 360°F (180°C). Bake for 13–15 minutes, until the edges are lightly golden and the center is set.
Cool. Let the cake cool in the pan for 10–15 minutes, then remove and leave on a rack until fully at room temperature.