Preheat oven to 375 degrees F and grease a 9×13 baking dish with the 2 tablespoons melted butter.
Separate the rolls and cut an X into the top each one, careful not to cut through the bottom. Use the handle of a wooden spoon to widen the hole, making room for the filling. Arrange rolls evenly in the baking dish.
In a small bowl, combine the ½ cup melted butter, brown sugar, cinnamon, and nutmeg and stir until smooth. Pour mixture over the rolls.
In another small bowl, beat the softened cream cheese until smooth, then stir in the sugar and egg.
Transfer cream cheese mixture into a piping bag or large ziplock with the corner snipped. Starting at the base of the hole, fill the rolls to the top with the cheesecake mixture. Alternatively, you can spoon the filling into the rolls, but we’ve found the bag method works best.