Preheat the oven to 375°F. Melt 1 tablespoon of butter and spread it evenly in a 9×13-inch baking dish.
Place the rolls over the butter and cut an X into the rolls about 2/3 down but not completely through the bottom.
Stir together the 1/3 cup butter, brown sugar, nutmeg, and cinnamon, then pour this luscious mixture over the rolls.
Next, stir the cream cheese until smooth. Add the sugar and beaten egg until fully incorporated.
Now, fill the rolls with this wonderful cream cheese mixture! You can use a piping bag or a spoon to get it just right.
Bake in the preheated oven at 375°F for 12 to 15 minutes, until they are golden brown and fragrant.
Allow the rolls to cool for a couple of minutes before serving. You can store any leftovers in an airtight container for a delightful treat later on!