In a large pot of boiling salted water, cook the pasta al dente according to package instructions. Reserve 1 cup of the cooking water, drain and set aside.
Heat the same pot used for the pasta over medium-low heat. Add the milk, greek yogurt, butter, salt, pepper, mustard and paprika. Whisk together until combined and heated through, about 5 minutes.
Add the cooked pasta and ½ cup of the reserved pasta water, and toss to fully coat for about 2 minutes.
Turn off the heat and stir in the cheese until melted completely. Add more pasta water to adjust if needed, and serve immediately.