Bring large pot of salted water to boiling over high heat. Add spaghetti and cook according to package instructions. Reserve 1 cup pasta cooking water, then drain pasta.

Meanwhile, in large high-sided skillet, heat butter over medium-low heat. Add garlic; cook 1 minute, stirring constantly. Whisk in yogurt, Parmesan cheese, milk, salt and black pepper. Cook 2 minutes or until warmed through, whisking constantly.

Add drained pasta and 1/2 cup pasta water to yogurt mixture; toss to combine. If sauce is too thick, add additional pasta water a splash at a time until desired consistency is achieved. Serve pasta sprinkled with additional Parmesan cheese, and parsley and red pepper flakes, if desired.