Preheat oven to 350°F (175°C). Grease a 9x13 inch baking pan thoroughly with butter or cooking spray, then dust lightly with flour, tapping out any excess.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, nutmeg, cinnamon, and cloves until the spices are evenly distributed. Set aside.
In a large mixing bowl, beat the softened butter and granulated sugar with an electric mixer on medium-high speed for 3-4 minutes until light, fluffy, and pale in color. Scrape down the sides halfway through.
Add the eggs one at a time, beating well after each addition until fully incorporated. Scrape down the bowl after adding all the eggs. The mixture may look slightly curdled, which is normal.
In a separate measuring cup or small bowl, combine the eggnog, milk, vanilla extract, and rum extract (if using). Stir until well combined.
With the mixer on low speed, alternate adding the dry and wet ingredients: add one-third of the flour mixture, then half of the eggnog mixture, then another third of flour, then the remaining eggnog, then the final third of flour. Mix only until each addition is just incorporated, then fold gently with a rubber spatula.
Pour the batter into the prepared pan and spread it evenly with a rubber spatula. Gently tap the pan on the counter a few times to release any large air bubbles, then smooth the top.
Bake in the center of the preheated oven for 32-38 minutes if using a 9x13 pan, or 28-32 minutes if using round pans, until a toothpick inserted in the center comes out with just a few moist crumbs.
Remove the cake from the oven and place the pan on a cooling rack. Let it cool in the pan for about 15 minutes, then turn it out onto a serving plate or let it cool completely in the pan before cutting. Dust with powdered sugar if desired and cut into squares.