Cook the spaghetti in salted water until al dente. Save 1/3 cup pasta water, then drain.
Season the chicken with paprika, Italian seasoning, garlic powder, black pepper, and 1/2 teaspoon salt.
Heat the olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Cook the chicken for 3 to 4 minutes per side until golden-brown and cooked through. Remove from the skillet.
Lower the heat to medium. Add the remaining butter and garlic and cook for 30 seconds. Stir in the sun-dried tomatoes and spinach until the spinach wilts.
Pour in the heavy cream and add the cream cheese. Stir over low heat until smooth.
Add the mozzarella and Parmesan and stir gently until melted into a thick, creamy sauce. Add a splash of pasta water if needed.
Toss the spaghetti in the sauce until every strand is well coated.
Serve the creamy spaghetti on one side of the plate and the garlic butter chicken separately alongside it. Finish with parsley and extra Parmesan if you like.