Cook the tortellini: Bring a large pot of salted water to a boil. Cook the tortellini according to package directions until just al dente. Reserve 1/2 cup pasta water, then drain.
Warm the chicken: If using rotisserie or pre-cooked chicken, chop or shred it and set aside.
If the chicken is cold, you can warm it gently in a skillet or let the hot sauce heat it through later.
Make the roux: In a large, deep skillet or pot, heat the olive oil or butter over medium. Whisk in the flour and cook for 1–2 minutes, stirring, until it smells nutty and looks smooth. Do not let it brown too much.
Add the milk: Slowly whisk in the milk, breaking up any lumps.
Keep whisking until the sauce begins to thicken, 3–5 minutes. Adjust heat to medium-low if it simmers too hard.
Season the base: Whisk in the Dijon, garlic powder, onion powder, smoked paprika (if using), 1/2 teaspoon salt, and a few grinds of black pepper.
Melt in the cheese: Turn heat to low. Add the cheddar and Parmesan a handful at a time, whisking until melted and smooth before adding more.
If the sauce seems too thick, splash in a bit of the reserved pasta water.
Stir in Greek yogurt: Remove the pan from heat and whisk in the Greek yogurt until fully blended. This keeps the tang fresh and prevents curdling. Taste and adjust salt and pepper.
Combine: Add the cooked tortellini and chicken to the sauce.
Fold gently to coat. If you’re adding peas or spinach, stir them in now. If needed, loosen with a little pasta water until creamy and glossy.
Finish and serve: Let everything sit on low heat for 1–2 minutes to warm through.
Top with a sprinkle of extra Parmesan and black pepper. Serve hot.