Cook the pasta: Bring a large pot of salted water to a boil. Cook pasta until just shy of al dente (1–2 minutes less than the package says).
Drain and set aside. Toss with a small splash of olive oil to prevent sticking.
Season the shrimp: Pat shrimp dry. Toss with 1/2 tsp salt, 1/4 tsp black pepper, smoked paprika, and red pepper flakes if using.
Sear the shrimp: Heat 1 tbsp olive oil in a large skillet over medium-high.
Add shrimp in a single layer. Cook 1–2 minutes per side until just opaque and lightly browned. Remove to a plate.
Do not overcook.
Warm the milk base: Lower heat to medium. In the same skillet, add minced garlic; sauté 30 seconds. Whisk in milk, Dijon, onion powder, and cornstarch.
Simmer gently 2–3 minutes, stirring, until slightly thickened.
Blend the creamy mix: In a blender, combine warm milk mixture, cottage cheese, and Greek yogurt. Blend until completely smooth and velvety, about 30–45 seconds. Return to the skillet over low heat.
Melt in cheeses: Add cheddar, mozzarella, and Parmesan in handfuls, stirring constantly on low heat until melted and glossy.
Season with salt and pepper to taste. If too thick, splash in a bit more milk; if too thin, simmer gently a minute.
Combine: Add cooked pasta and shrimp to the sauce. Stir to coat evenly.
Finish with lemon juice for brightness and adjust salt/pepper.
Optional bake: For a crunchy top, transfer to a broiler-safe dish. Sprinkle oiled panko and a little extra Parmesan. Broil 1–2 minutes until golden.
Watch closely.
Garnish and serve: Top with parsley or chives. Serve hot.