Add homemade eggnog to a pan and heat on high until it begins to simmer. Reduce heat to medium and simmer until eggnog has thickened and reduced – about ten minutes. Set aside and let cool completely. While eggnog is cooling, make the brownie batter. Sift together flour, cocoa powder, baking powder and salt and mix to combine, set aside. Beat together butter, sugar, vanilla and add one egg at a time. Add the dry ingredients into the wet ingredients in two installments. Reserve 1/2 cup of the brownie batter for swirling. Spread remaining batter into prepared pan.
Beat chilled eggnog, cream cheese and egg until smooth. Spread cheesecake mixture onto brownie batter. Dollop reserved brownie batter over cheesecake mixture and swirl with the back of a knife. Bake for 35-40 minutes or until the sides begin to pull away from the side of the pan.