Set a large, heavy pot over medium heat.
Add the butter and olive oil. When the butter melts, add the minced garlic. Cook 30–60 seconds until fragrant, stirring so it doesn’t brown.
Pour in the broth, milk, salt, pepper, and red pepper flakes if using.
Stir and bring to a gentle simmer.
Add the dry pasta. Stir well to prevent sticking. Keep the liquid at a steady simmer, not a hard boil.
Cook uncovered, stirring every 2–3 minutes, until the pasta is al dente and the liquid has reduced into a creamy base, about 10–12 minutes.
If the pot looks dry before the pasta is done, add a splash of broth or water.
Reduce the heat to low. Stir in the heavy cream if using. Simmer 1–2 minutes to thicken slightly.
Turn off the heat and add the Parmesan.
Stir until fully melted and the sauce is glossy. If the sauce seems too thick, loosen with a bit more milk or hot water.
Taste and adjust seasoning. Add the lemon juice if you like a brighter finish.
Let the pasta sit for 2 minutes to set up, then garnish with parsley and extra Parmesan.
Serve right away.