Bring a large pot of salted water to a boil. Cook spaghetti according to package directions until al dente. Reserve 1 cup pasta water before draining.
While pasta cooks, mince the garlic cloves finely.
In a large skillet, melt butter over medium heat. Add minced garlic and cook for 1-2 minutes until fragrant and golden. Be careful not to burn it.
Pour in the heavy cream and bring to a gentle simmer. Cook for 3-4 minutes until slightly thickened.
Add the cooked pasta to the skillet. Toss everything together, adding pasta water a splash at a time until the sauce coats the pasta beautifully.
Remove from heat. Stir in grated Parmesan cheese, salt, pepper, and fresh parsley. Serve immediately.