Combine milk and broth in a bowl or measuring cup; set aside.

Bring a large pot of salted water to a boil and cook the pasta to al dente. Drain and set aside.

In a large saucepan, melt butter over medium heat. Whisk in flour and cook 1–2 minutes until lightly golden. Gradually whisk in the milk-broth mixture until smooth and cook until slightly thickened, about 4–5 minutes.

Reduce heat to low. Stir in Greek yogurt, Dijon, and seasonings until smooth.

Add the cheeses a handful at a time, stirring gently until melted and creamy.

Add the pasta and stir to coat evenly. Let sit for 1–2 minutes so the sauce thickens and clings to the pasta.

Optional: Transfer to a baking dish, top with a little extra cheddar or parmesan, and broil for 2–3 minutes until golden and bubbly.

Finish with additional salt and pepper to taste and serve immediately.