Boil the pasta. Bring a large pot of salted water to a boil. Cook pasta until just al dente.
Reserve at least 1 cup of the starchy cooking water, then drain.
Warm the aromatics. In a large skillet over medium heat, melt butter or warm olive oil. Add garlic and cook 30–60 seconds until fragrant, not browned.
Make the yogurt base. In a mixing bowl, whisk Greek yogurt, Parmesan, lemon juice, black pepper, and a pinch of salt. Set aside.
Create the sauce. Reduce the skillet heat to low.
Add 1/2 cup pasta water to the garlic pan. Whisk in the yogurt mixture off the heat or over very low heat until smooth and creamy. Adjust salt and lemon to taste.
Toss with pasta. Add the drained pasta to the skillet.
Toss gently, adding more pasta water a splash at a time until the sauce coats every strand and looks glossy.
Add protein and veggies (optional). Fold in cooked chicken, shrimp, spinach, broccoli, or peas. Warm through on low heat for 1–2 minutes. Do not let the sauce simmer.
Finish and serve. Top with extra Parmesan, parsley, and red pepper flakes if you like.
Serve immediately while creamy.