Warm the butter and milk in a saucepan over medium low heat until butter is melted and mixture just starts steaming. Set aside to cool slightly, to 120-130 degrees F.

Add the warm butter mixture and egg and mix to make a wet dough.

With the mixer running, add remaining flour 1/4 cup at a time until dough mostly clears the bowl but still feels sticky. Knead the dough a few minutes more until smooth and elastic.

Cover with plastic wrap and let rise in a warm place until doubled, about 1 hour.

Gently punch down the dough to release gases and knead to bring back into a ball. Let sit for a few minutes while you get the filling ingredients ready.

On a lightly floured surface, roll out the dough into a rectangle roughly 12x17 inches. No need to be exact.

Spread melted butter evenly over the rolled dough. Sprinkle with brown sugar and ground cinnamon.

Starting with one long end, gently roll up dough into a log. Using a sharp knife or unscented floss, remove ends to make a clean edge and cut into 11 rolls.

Place on a sheet pan lined with parchment (see Notes) about 1 1/2 - 2 inches apart to make a tree shape: 1 roll on top row, 2 rolls in next row, 3 rolls in next row, 4 rolls in next row, and 1 roll for the trunk at the bottom.

Cover with plastic wrap and let rise in a warm place until doubled again, 20-30 minutes. Meanwhile, preheat oven to 350 degrees F.

Bake until cinnamon rolls are golden brown, 22-25 minutes.

In a bowl with an electric mixer, beat the butter, cream cheese, powdered sugar, and milk or eggnog until smooth and creamy. Add more milk or eggnog if needed to get a spreadable consistency.

Spread over warm or cooled rolls. Sprinkle with holiday sprinkles if desired.