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 it quickly by setting the bowl in cold water.
8 tbsp 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 extract until incorporated.
1⅓ tbsp honey, ½ tsp vanilla extract
Add dry ingredients. Sift the almond flour, cake flour, and baking powder together, then mix into the wet ingredients until smooth.
¾ cup almond flour, 9 tbsp cake flour, 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 the butter isn't too hot before adding 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
Fill the pan. Pour the batter in — it will be fairly fluid.
Bake. 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 before removing.