Soft and fluffy cinnamon rolls made with eggnog in the dough and in the brown butter frosting!
In a small measuring cup, add the sugar and yeast to the warm water. Allow to activate for 5-10 minutes.
Place the eggnog and butter in a skillet. Warm until the butter is mostly melted. Make sure the eggnog isn't above 105° F or it will kill the yeast. Add to the bowl of a stand mixer. Add the flour, egg, salt, and yeast mixture, in that order.
Using the paddle attachment, mix just until a shaggy dough forms. Switch to the dough hook and knead for 15 minutes, or until the dough is smooth and elastic. You can add up to 1/2 cup more flour if needed to get the dough to the proper consistency. The dough should be quite soft and not completely clean the bottom of the bowl, but not so sticky that it doesn't form a dough.
Butter a large bowl. Form the dough into a ball, place it top-side-down in the bowl, and flip it to grease the top of the dough. Cover and let rise in a warm spot until doubled, about 1 1/2 to 2 hours.
In a small bowl, mix together the brown sugar and cinnamon very well.
Roll the dough out to a 12"x17" rectangle on a generously buttered work surface with a buttered rolling pin. Spread the browned butter across the dough, making sure to leave 1 inch of the dough clean at the far long end. Sprinkle the cinnamon sugar mixture evenly across the butter on the dough. Roll up jelly-roll style along the long end closest to you. Pinch the seam to seal.
Slice the dough log cross-wise into 15 rolls (about 1 inch wide). Transfer to a buttered 13x9-inch baking dish (arrange them 3 across, 5 down). Cover and allow to rise in a warm spot until almost doubled, about 1 to 2 more hours.
Half an hour before the rolls are done rising, preheat your oven to 375° F. Bake the risen rolls for 20-30 minutes, or until they're golden brown and an instant read thermometer inserted into one of the rolls registers 200° F. Remove from oven and allow to cool for 15-20 minutes.
In a small bowl, whisk together all of the frosting ingredients very well until smooth. Drizzle over the rolls while they're still warm (but not hot).
Serve the rolls warm with butter.
If you're unsure what browned butter is, check out my How to Brown Butter post for all the details!