Cook the pasta: Bring a large pot of salted water to a boil.
Cook pasta until just shy of al dente, 1 to 2 minutes less than package directions. Reserve 1 cup pasta water, then drain.
Season the chicken: Pat chicken dry and cut into small bite-size pieces. Toss with 1 teaspoon kosher salt, 1/2 teaspoon black pepper, 1/2 teaspoon garlic powder, and 1/2 teaspoon smoked paprika.
Sear the chicken: Heat 1 tablespoon olive oil in a large skillet over medium-high.
Add chicken in a single layer. Cook 4–6 minutes, stirring once or twice, until browned and cooked through. Transfer to a plate; tent with foil.
Make the protein base: In a blender, combine 1 cup cottage cheese and 1/2 cup Greek yogurt.
Blend until completely smooth. Set aside.
Build the roux: In the same skillet or a large pot, melt 2 tablespoons butter over medium heat. Whisk in 2 tablespoons flour and cook 1–2 minutes until lightly golden and nutty.
Create the sauce: Slowly whisk in 1 cup milk and 1/2 cup chicken broth.
Simmer 2–3 minutes until slightly thickened and glossy.
Add flavor: Whisk in 1 teaspoon Dijon mustard, 1/2 teaspoon onion powder, 1/2 teaspoon garlic powder, and a pinch of smoked paprika. Taste and season with salt and pepper as needed.
Melt the cheese: Reduce heat to low. Add 1 1/2 cups shredded sharp cheddar and 1/2 cup shredded mozzarella.
Stir until melted and smooth.
Boost with protein base: Whisk in the blended cottage cheese–Greek yogurt mixture until fully incorporated and silky. If too thick, loosen with splashes of reserved pasta water or milk.
Combine: Add the drained pasta and cooked chicken to the pot. Toss until everything is well coated.
If using veggies (like 1 cup peas or steamed broccoli), fold them in now.
Finish: Stir in 2 tablespoons finely grated Parmesan for extra punch, if desired. Adjust seasoning. The sauce should be creamy and coat each noodle without pooling.
Optional bake: For a baked version, transfer to a greased dish, top with a light sprinkle of cheddar or whole-wheat breadcrumbs, and bake at 375°F for 12–15 minutes until bubbly and lightly golden.