Bring a large pot of salted water to a boil and cook the spaghetti according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain the pasta.
In the same pot, melt the butter and olive oil over medium heat. Add the minced garlic and sauté for about 1-2 minutes until fragrant (be careful not to burn).
Pour in the heavy cream and stir well, allowing it to simmer for about 2-3 minutes until slightly thickened.
Reduce the heat to low and gradually whisk in the grated Parmesan until it melts smoothly into the cream mixture.
Add salt, pepper, and red pepper flakes (if using) to taste. If the sauce is too thick, gradually add some reserved pasta water until you reach your desired consistency.
Add the drained pasta to the sauce, tossing to coat all the noodles evenly. Cook together for an additional minute to heat through.
Serve hot, garnished with fresh parsley and extra Parmesan, if desired.