Bring a large pot of salted water to a boil and cook pasta until al dente. Reserve 1 cup pasta water, then drain.
In a large skillet, melt butter with olive oil over medium heat.
Add garlic and sauté gently until fragrant, about 30 seconds.
Pour in the cream and simmer gently for 3–4 minutes until slightly thickened.
Remove from heat and stir in Parmesan cheese until smooth.
Add cooked pasta and toss to coat, adding pasta water as needed.
Season with salt, pepper, and red pepper flakes if using.
Serve immediately.