After simmering the butter and heavy cream to thicken it, turn off the heat then stir in the cheese. You won't have any separation issues.

Combine cream and butter turn off heat and add cheese.  You'll know the cream is getting ready to break when you start seeing little beads of yellow butterfat separating from the cream around the edge of the pan.This is the time to remove the pan from the heat, add the cheese, and flip and roll the pasta to incorporate and melt the cheese into the sauce.

If your sauce breaks, there is an easy save. Just add some more cream, bring it back to a boil, roll and stir it, then plate the dish.

salt to taste

You can add whatever to it, especially fresh ground black pepper and/or nutmeg
but that's the basic recipe.
Heat but not boil, til well blended and serve over/in pasta
Red pepper flakes are good in it also.