Heat the eggnog and butter in a glass cup in the microwave until the butter is melted (you can also heat these in a pan on the stove, if desired). Cool to 110 to 115℉ (about as warm as you'd like a bath to be, if you don't have a thermometer).
In the bowl of a stand mixer, combine the warmed eggnog mixture with the yeast. Let sit for a minute or two, then add the egg, 2 cups of flour, salt and nutmeg. Use the dough hook of your mixer to combine the ingredients. Add remaining flour (up to 3 cups), ½ cup at a time while the dough hook is stirring. Stop the mixer to scrape down the sides of the bowl, as needed. The dough hook should be pulling the dough up out of the bowl and away from the sides. If it's still too sticky, add additional flour by the tablespoon until you get the desired consistency. Let the dough hook knead the dough for 5 minutes.
Turn the dough onto a lightly floured surface and work with your hands a little bit to form a smooth, round ball. Coat a large bowl with nonstick spray. Place dough in the bowl and turn it over to coat with the spray. Cover the bowl with a clean dish towel. Place it in a warm place to rise until the dough doubles in size, about 1 hour (see tips below).
MAKE THE OOEY GOOEY COATING:
In a medium bowl, whisk together the brown sugar, cinnamon and nutmeg. Place the melted butter in a separate bowl.
FORM THE BREAD BALLS:
Spray a bundt pan with nonstick spray.
Remove the dough from the bowl onto a lightly floured surface and gently pat it into an 8-inch square. Using a sharp knife or a bench scraper, cut the dough into 64 pieces (cut the square into 4 pieces, then cut each piece into 16 pieces).
Roll each small piece into a ball. Dip a ball in the melted butter, then roll in the brown sugar mixture; place it into the bundt pan. Continue with the remaining 63 pieces of dough, layering the balls as they accumulate in the bundt pan. If you have any melted butter left over, drizzle a couple of tablespoons over the layered dough balls.
Cover the bundt pan with a clean dish towel, and place it back into a warm place to rise for about another hour. They should get slightly puffier.
BAKE:
Preheat your oven to 350℉ (if you're using the oven as a warming place, take out the bundt pan before you preheat the oven!)
Remove the dishtowel. Bake about 30 minutes, or until the top has browned and ooey gooey caramel is bubbling around the edges. Cool in the pan for 2 to 3 minutes, then flip the bundt pan upside down onto a platter to remove the contents of the pan. Let it sit on the platter for a few minutes to cool slightly before glazing.
ADD THE GLAZE:
Whisk together the powdered sugar, eggnog and nutmeg.
Spoon the glaze over the top and sides of the monkey bread. Serve warm; it's ready to pull apart and eat!
Notes
You can certainly mix and knead the dough by hand. It'll just take some arm strength to get the job done!
My favorite place for rising bread dough is in my (cold) oven. You can make a cold oven a slightly warm place by turning on the oven to 400 degrees F. and letting it warm up for ONE MINUTE ONLY. Then TURN IT OFF. Turn ON the oven light. Now you've got a warm place for rising. MAKE SURE THE OVEN IS TURNED OFF THOUGH!