Prep pan and oven. Heat oven to 325°F and arrange rack in the middle. Grease a 9 x 13-inch baking pan with baking spray or oil and set aside.

Separate eggs. Gently crack eggs into the bowl of a stand mixer fitted with the whisk attachment. Do this carefully so you don't break the yolks. If you break a yolk you'll have to start over. Gently remove the yolks with your hands, scooping them up and letting the whites run through your fingers. Place yolks in a large bowl—make sure the bowl is big enough to mix all the cake batter eventually. *Once again: important that you don't get any trace of egg yolk in the whites or they won't whip up to stiff peaks. I know this method of separating eggs might sound weird, but it actually is the most gentle way of dividing the yolk from the white.

Beat egg yolks. Add sugar, pumpkin puree, and 1 teaspoon of the vanilla to the egg yolks and whisk until thick, creamy, and the sugar is mostly dissolved, about 3 minutes.

Whip egg whites. In the stand mixer, whip the egg whites on medium speed until they are stiff, but not dry, about 6 minutes.

Fold eggs together. Add about 1/3 of the egg whites into the yolks and fold gently with a rubber spatula. Add remaining whites and gently fold until only a few largish pieces of egg white remain.

Add flour. Place a large metal sieve on a piece of parchment paper. Add flour, baking powder, salt, 2 teaspoons of the cinnamon, cardamom, nutmeg, ginger, and cloves. Sift the flour into the egg mixture by gently tapping the side of the sieve until it all goes through. Rub any clumps that remain through the sieve to get it to go through. Pour any leftover bits into the bowl and gently fold that in as well being careful not to deflate the egg whites too much.

Bake. Spread the batter evenly in the pan and bake in the middle of the oven until the top of the cake is golden around the edges and springy to the touch. A toothpick inserted in the middle should come out clean, about 25 minutes.

Make tres leches mixture. While cakes are baking, whisk together the sweetened condensed milk, the evaporated milk, and 1/2 cup of the heavy cream in a large bowl.

Pour milk over cake. Let cake cool 15 minutes (cake will pull away from the sides of the pan) then poke cake all over with a skewer or fork. Pour milk mixture over cake. Cake will float in the milk mixture but will eventually soak most of it up. Let cake cool for another 30 minutes at room temperature then cover with plastic wrap and refrigerate for at least 4 hours but best overnight.

Make whipped cream topping. Combine remaining 2 cups heavy cream, powdered sugar, and remaining 1 1/2 teaspoon of the vanilla extract in the bowl of a stand mixer and whip with the whisk attachment until fluffy pillowy peaks form.

Decorate cake. Spread cream evenly over cake then dust with remaining 1/2 teaspoon ground cinnamon. You can use as much or as little cinnamon as you'd like. I like to keep it on the light side, around a teaspoon total. Cut into squares and serve.