Preheat your oven to 325 degrees. Line an 8x8" baking dish with parchment paper (or use a silicone baking dish and give it a light spray with cooking spray).
Separate egg whites and yolks into two separate bowls. Beat the egg whites with an electric mixer until whites form still peaks. Set whites aside.
Mix together yolks, sugar, butter, cinnamon, and vanilla. Slowly mix in flour until there are no lumps. Slowly add eggnog (this will make batter thin).
Gently fold in the egg whites. Whites do not have to be completely mixed in; you might see some lumps of egg white.
Bake for 60 minutes at 325 degrees, until top turns brown and cake is set. Allow to cool for 30 minutes before dusting with powdered sugar, cutting with a sharp knife, and serving warm.