Heat a large pot of water with a tablespoon of salt. Once boiling, add pasta and cook until al dente, about 10-12 minutes. Drain but keep about 1 cup of the pasta water for later.
Heat a large skillet or braising dish over medium heat. Add olive oil and butter. Once butter has melted, add minced garlic and cook until garlic begins to turn slightly golden, about 2-3 minutes.
Add cream to skillet and cook until thickened and when the butter has mixed into the cream, about 8 minutes. Reduce heat to medium-low and sprinkle in the Parmesan cheese. Stir together and let the sauce come back to a simmer. Reduce heat to low. Taste sauce and add salt and pepper, if needed. Add pasta and toss together until combined. Remove from heat once pasta is coasted and heated through.
If the sauce gets too thick, add a little of the reserved pasta water to thin it out. Garnish with chopped parsley and serve immediately.