Preheat the oven to 350°F (175°C).
Cook the spaghetti according to package instructions until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add the chopped onion and green bell pepper and sauté for 5 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the shredded chicken, diced tomatoes with green chilies, chicken broth, smoked paprika, cayenne pepper, chili powder, black pepper, and salt. Cook for 5 minutes, stirring occasionally.
Reduce heat to low and add the cream cheese. Stir until the cream cheese is fully melted and combined.
Remove the skillet from heat and stir in the cooked spaghetti, half of the cheddar cheese, and half of the Monterey Jack cheese until evenly mixed.
Transfer the mixture to a greased 9×13 inch casserole dish.
Sprinkle the remaining cheddar and Monterey Jack cheese evenly over the top.
Bake uncovered for 20 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let it cool for 5 minutes.
Garnish with chopped fresh parsley before serving.