Boil the pasta. Bring a large pot of well-salted water to a boil. Cook pasta until just shy of al dente. Reserve 1 to 1.5 cups of the starchy pasta water, then drain.

Prep the yogurt mixture. In a bowl, whisk Greek yogurt with 1/4 cup of the reserved pasta water, 1/2 cup grated Parmesan, lemon zest, and a pinch of salt and pepper. Set aside. This tempers the yogurt so it blends smoothly later.

Sauté the garlic. In a large skillet over medium heat, melt the butter with the olive oil. Add minced garlic and cook 30–60 seconds until fragrant, not browned. If using red pepper flakes, add a pinch now.

Add pasta to the pan. Toss the drained pasta into the skillet with the garlicky butter. Add 1/4 to 1/2 cup reserved pasta water to loosen.

Fold in the yogurt sauce off heat. Turn off the heat. Add the yogurt-Parmesan mixture to the pasta and toss quickly and gently until the sauce turns silky and coats the noodles. If it looks too thick, splash in more pasta water a little at a time.

Finish with flavor. Stir in another 1/4 cup Parmesan (or more to taste) and 1–2 teaspoons lemon juice. Season with salt and plenty of black pepper. The sauce should be glossy and clingy, not tight or soupy.

Serve. Plate immediately. Top with extra Parmesan and chopped parsley if you like. Serve warm.