Melt butter in a small saucepan over medium low heat. Once butter is melted, add the eggnog and heat for 1 minute more (mixture should be between 120-130°F).
Pour mixture into bowl of electric mixer and whisk in egg and yeast. Add 2 ½ cups (325 grams) flour, sugar, and salt. Use dough whisk or wire whisk to combine to make a wet shaggy dough.
Fit mixer with dough attachment and knead dough on low speed, adding remaining flour ¼ cup (35 grams) at a time while kneading, waiting until flour is incorporated before each addition. Add just enough flour so the dough clears the sides of the bowl, and still feels soft and tacky to the touch, but doesn’t stick and come off on your fingers (you may need slightly more or less than 3 ½ cups flour). Continue to knead dough until smooth and elastic, about 8-10 minutes total kneading time.
Bring dough into a ball, then cover and let it rise in a warm place until doubled, about 1 hour (or 30 minutes if using instant yeast).
Gently punch down the risen dough and knead it with your hands a few times. Shape back into a ball and let it rest for a few minutes while you prepare the cinnamon roll filling. Melt butter, and combine 6 Tbsp. granulated sugar with cinnamon and nutmeg in a separate bowl.
On a lightly floured surface, roll dough out into an approximate 12x17-inch rectangle, adding flour as needed to keep it from sticking. (If dough springs back and doesn’t roll out easily, cover with a towel and let it sit for 15 minutes before trying again.) Brush dough with melted butter to the edges and sprinkle evenly with the cinnamon-sugar mixture.
Starting with a long edge, gently roll up the dough into a long log, careful not to push filling out as you go. Using a sharp knife or unscented floss, trim ends of the log so you have flat edges on each side. Slice dough into 2 equal halves, and then divide each of those pieces in half again, and finally divide those into 3 rolls each about 1 ½ inches wide. You should have 12 rolls.
Place sliced rolls evenly-spaced into a greased 9x13-inch pan. Cover with plastic wrap and let rolls rise until puffed and almost doubled in size, about 20-30 minutes. Meanwhile, preheat the oven to 350°F.
Bake rolls until the tops just begin to turn golden brown, about 20-25 minutes. (Do not over-bake rolls or you’ll lose the soft gooey centers.)