Preheat your oven to 375°F. Melt 1 tablespoon of butter and coat a 9x13-inch baking dish evenly with it.
Arrange the rolls on the buttered dish. Cut an X about two-thirds down the rolls, but don't slice them all the way through.
In a measuring cup, combine the melted butter, brown sugar, nutmeg, and cinnamon. Pour this mix generously over the rolls.
Blend the softened cream cheese until smooth, then mix in the granulated sugar. After it’s smooth, add in the beaten egg and combine until fully incorporated.
Carefully fill each roll with the cream cheese mixture. Using a piping bag works best, but a zip-top bag with the corner cut can do the trick too. If you're using a spoon, take a little extra time to stuff them good!
Bake the rolls uncovered in the oven for 12 to 15 minutes, depending on how golden you like them. For softer rolls, around 12 minutes is perfect.
Once done, let them cool for a couple of minutes before digging in; the filling will be very warm.