Preheat oven to 325 degrees F.
Line an 8-inch square cake pan or dish with aluminum foil or parchment paper. If using aluminum foil, coat the foil with cooking spray or baking spray.
Separate the eggs; place the egg yolks in a large mixing bowl with the sugar. Place the egg whites in another large mixing bowl.
Beat the egg yolks and sugar on high speed with an electric mixer for 2 minutes. Mixture will be thick and lemon-colored. On low speed, gradually add the melted butter and vanilla, scraping down the sides as needed.
Add the flour and cocoa powder to the egg yolk mixture. Beat just until flour is combined. Gradually add the milk, beating just until combined.
Wash the beaters thoroughly so there’s no chance of getting any egg yolk in the egg whites. Beat the egg whites on medium speed of the mixer until foamy; add the cream of tartar. Increase the speed to high and beat until the egg whites form stiff peaks, about 2 minutes.
Whisk about one-third of the egg whites into the thin batter. Tip: I just take off the two beaters from the mixer to avoid washing another utensil.
Gently fold the remaining egg whites in with a flexible spatula. It’s ok if there are still a few streaks of egg whites. Pour the batter in the prepared cake pan.
Bake at 325 degrees for 38 to 40 minutes, or just until the center jiggles slightly when gently shaken. If it doesn’t jiggle at all, it has baked too long. It will firm up when chilled.
Let the cake cool completely on a wire rack, about 1 hour. Cover and refrigerate at least 2 hours to chill thoroughly. Using the overhang of aluminum foil or parchment paper, lift the cake out of the pan and cut into 9 squares. You should see 3 distinct layers. Sprinkle with 1 teaspoon cocoa powder, if desired.