Boil salted water in a 3-quart pot. Add spaghetti and cook for about 7-8 minutes, until al dente. Drain, reserving 1 cup of pasta water.
In a 10-12 inch saute pan, melt butter and olive oil over medium heat. Add garlic and stir, cooking for about a minute.
Add spaghetti, 1 cup of pasta water, cream cheese and heavy cream to the skillet. Bring to a boil and add shredded cheeses. Stir constantly until cheeses are melted and pasta is completely coated; about a minute. Reduce heat and continue to cook and stir until sauce is thickened and reduced; about 1-2 minutes.
Remove from heat and stir in parsley. Taste and add salt and pepper as desired.
Serve hot, and garnish with more fresh parsley and some fresh grated Parmesan, if desired.