Cook the Pasta — Fill a large pot with salted water and bring to a boil, Cook the pasta according to the package instructions until al dente. Keep some pasta water before draining.
Sauté the Garlic – Melt the butter in a large pan over medium heat. Add the minced garlic, and cook for about 1 minute, stirring often, until fragrant but not browned.
Stir in the Milk & Greek Yogurt – After lowering the heat to low, and slowly, stir in the milk and then the Greek yogurt. Keep whisking to form a smooth paste and avoid curdling.
Add the Cheese — Add the grated Parmesan (or Pecorino Romano) little by little, stirring vigorouslly until completely melted and the sauce is creamy. Add reserved pasta water, as needed, to loosen consistency.
Combine with Pasta – Toss in the drained pasta, gently turning it over to coat every strand with creamy sauce. Let it simmer for a minute or two so the pasta takes on some flavor.
Finishing & Serving – Just about to stir in the finely chopped parsley for a hint of freshness. Taste and adjust seasoning if necessary, then serve immediately, with extra cheese on top. Enjoy!