Preheat oven to 425º F. Melt 1/2 cup (1 stick) of butter in a bowl, let cool (use this bowl for each step when you need melted butter).
Brush 1 Tbsp of butter into a 9 inch cake pan or pie plate. Set aside.
Prepare the filling. In a bowl combine brown sugar, sugar, cinnamon, nutmeg, cloves, and salt. Add 1 Tbsp melted butter. Using your fingers or a fork stir together until is feels like wet sand. Set aside.
Prepare the dough. In a large bowl, whisk together flour, sugar, baking powder, baking soda, and salt.
In a liquid measuring cup mix together eggnog and 2 Tbsp melted butter. Add the milk mixture to the flour mixture and stir with a wooden spoon, until everything is combined (about 30 seconds). The dough will be very rough.
Turn onto a floured surface and kneed until just smooth (handle as little as possible for flaky rolls).
Using your hands, press the dough into a 12x9 inch rectangle.
Brush with 2 Tbsp melted butter. Sprinkle the filling evenly over the dough, pressing gently into the dough. Be sure to leave about 1/2 in border around the edges. Using a scarper loosen the dough from the counter, and roll (starting from the long side), into a tight cylinder. Pinch to seal.
Using a sharp knife, cut into 8 equal pieces. Slightly flatten each piece of dough, to try to keep the filling in. Place 1 roll in the center of the prepared pan, and arrange the other 7 around it. Brush with the last 2 Tbsp of butter.
Bake for 20-25 minutes until the edges are golden brown. Allow the rolls to rest for 5 minutes before frosting.
Meanwhile, prepare the icing. In a small bowl mix all of the icing ingredients together. You can adjust the eggnog and sugar level to get the desired consistency. Drizzle the icing over the cinnamon rolls.