Cook the chicken. Add the chicken breasts to the slow cooker in a single layer. Then, add butter, Worcestershire sauce, salt, black pepper, granulated onion, paprika, garlic, Rotel, and heavy cream. Stir to combine, making sure the chicken is well-coated. Cover and cook on HIGH for 3-4 hours or LOW for 5-6 hours until the chicken is fully cooked and tender.
Cook the pasta separately. About 20 minutes before the chicken is finished, cook the spaghetti according to the package instructions. Drain the pasta and set aside.
Shred the chicken. Once the chicken is done cooking and tender, remove it from the slow cooker and place it in a medium-sized bowl. Then, shred the chicken using two forks. Set aside, leaving any liquids behind in the slow cooker.
Make the cheese sauce. Add the cream cheese and Velveeta (or shredded cheddar) to the slow cooker. Stir to add the cheese into the remaining liquid, then cover and cook on HIGH for 15 minutes until the cheese has fully melted and the sauce is smooth. Then, stir the mixture well to make sure the sauce is creamy and evenly combined.
Add the shredded chicken and pasta. Return the shredded chicken to the slow cooker and stir to combine it with the cheese sauce. Then, add the cooked spaghetti and gently stir everything together until the pasta is fully coated in the sauce.
Optional broiling step. For a cheesy, browned top, spoon the dish onto plates, sprinkle with extra shredded cheddar cheese, and broil for 1-2 minutes until the cheese is bubbly and golden. Be sure to observe to avoid burning.
Serve and garnish. Garnish with freshly chopped parsley if desired, and serve immediately. Alternatively, transfer the spaghetti mixture to a greased 13x9-inch baking dish, top with additional cheese, and bake at 350℉ for 20 minutes for a more casserole-style presentation.