Cook spaghetti until al dente. Reserve ½ cup pasta water before draining.
Season chicken with Italian seasoning, garlic powder, paprika, salt, and pepper.
Heat olive oil and 2 tbsp butter in a skillet. Sear chicken until golden-brown with crispy edges and cooked through. Remove and set aside.
Melt remaining butter in the same skillet. Add garlic and cook until fragrant.
Pour in heavy cream and stir in cream cheese until smooth.
Off the boil, stir in 1 cup Parmesan and 1 cup mozzarella until thick and glossy. Loosen with pasta water.
Toss spaghetti in the sauce until every strand is coated.
Top with reserved mozzarella, cover 2 minutes off heat until melted and stretchy.
Arrange chicken beside the pasta, dust with remaining Parmesan, finish with red pepper flakes and parsley.