Preheat the oven to 300 degrees F. Butter and flour an 8-inch square pan.
In a mixer fitted with a whisk attachment, beat the eggs at medium speed until fluffy and light yellow. Add both sugars. Add remaining ingredients, and mix to combine.
Pour the batter into a greased and floured 8-inch square pan and bake for 45 minutes. Check for doneness with the tried-and-true toothpick method: a toothpick inserted into the center of the pan should come out clean. When it's done, remove to a rack to cool. Resist the temptation to cut into it until it's mostly cool.