Warm the pot: In a large, wide pot or deep sauté pan, heat the butter and olive oil over medium heat until the butter melts and foams slightly.
Sauté the garlic: Add the minced garlic and cook for 30–60 seconds, stirring often.
Keep the heat moderate so it turns fragrant without browning. If it starts to color, lower the heat.
Add liquids: Pour in the chicken broth, milk, and heavy cream. Stir to combine, scraping up any garlic bits from the bottom.
Bring the mixture to a gentle simmer.
Add spaghetti: Add the spaghetti, breaking it in half if needed to fit. Submerge the pasta as much as possible. Stir to prevent sticking.
Simmer and stir: Cook uncovered at a steady simmer for 10–12 minutes, stirring every 1–2 minutes.
The sauce will thicken as the pasta releases starch. Adjust heat to keep it from boiling too vigorously.
Season and finish: When the pasta is al dente and the sauce has reduced, turn heat to low. Stir in the Parmesan, salt, black pepper, and red pepper flakes if using.
Add lemon zest for brightness, if you like.
Tweak the texture: If the sauce is too thick, add a splash of broth or milk. If it’s too thin, let it simmer another minute, stirring, until it clings to the noodles.
Serve: Taste and adjust seasoning. Plate the spaghetti and top with extra Parmesan and chopped parsley.
Serve immediately while creamy and hot.