Preheat oven to 325 degrees. Butter the sizes and bottom of a 2 quart baking dish (for me, this is an 8x11 glass rectangular dish, you may have oval).
Use a mixer to beat together eggs, white sugar and brown sugar until they are thick and light in color. This will take about 10 minutes.
Next, mix in vanilla extract.
Sift together the cocoa powder, all purpose flour and almond flour.
With the mixer on low speed, gradually beat in the flour mixture until all ingredients are just combined.
Keep the mixer on low speed and slowly beat in the butter until just combined.
Pour batter into prepared baking dish. Place prepared baking dish into a larger baking dish (for me, this was an 11x15 glass dish). In the large baking dish, put water until it reaches halfway up the side of your smaller dish. NOTE: The water goes in the large dish, NOT in the small dish with the batter.
Bake for 60 minutes (see notes above about time). The top will be crispy and the inside will look like a pudding or very underdone brownie.