Yes it would. Here's how you make a classic 4-cheese sauce:
It's really a variant of the bechamel, moving into the mornay sauce when you add cheese.
- 2 TB flour
- 2 TB butter
- 2 cups milk
- 2 ounces cheese
usually, I will add a little more butter (up to 1 TB) and more flour (up to 2 TB). I also start with 2 TB of garlic or shallots (depending on the dish) fried in the butter before adding flour. Cheese is to taste. And I finish with a dash of white pepper, a little nutmeg, and a teaspoon or so of dijon mustard, all whisked in the end.
melt butter, add flour and mix together. Let cook for a minute. Add the milk and whisk it all together. Bring to a boil. Turn down and let simmer for 10-15 minutes so mellow out the flour. Turn off, add cheese, whisk.
If you don't like the consistency, add a little milk if too thick, or add some beurre manie (softened butter/flour mix) if too thin.
What you did is start with an overly fatty mix of butter and cream. About the only way you could get that recipe to work is if you increased the protein solids but not the fat, such as by reducing down the cream by boiling it or adding whey protein solids. And no butter.
If you were melting the cheese and boiled it, that's drastically excessive heat. Hard to fix as the protein is damaged. You'd need to create a variant of processed cheese at that point.