Preheat the oven to 400°F. If you don't have a deep dish oven-safe skillet, butter a large casserole dish.
Bring a large pot of salted water to a boil over high heat. Boil the pasta until al dente, according to package directions. During the last 2 minutes of cooking, add the broccoli. Drain, add the pasta and broccoli back into the pot.
Add the cream cheese, mixing it into the pasta and allowing it to melt. Now add cottage cheese, milk, eggs, parsley, and parmesan. Mix it all together until creamy.
Meanwhile, in a large oven-safe skillet, melt the butter with the chicken, onion, thyme, paprika, garlic powder, cayenne, salt, and pepper. Cook until golden and the butter is toasted, 5-8 minutes.
Mix the pasta, broccoli, and cream sauce into the chicken. Only a gentle mix is needed! Top with both cheeses. Bake 20 minutes, until the cheese is melted and beginning to brown. Serve warm with additional thyme and fresh basil.