Place the chicken breasts in the base of a slow cooker insert.
In a separate bowl, thoroughly mix together the diced onion, bell pepper, minced garlic, diced tomatoes, both condensed soups, dried oregano, basil, kosher salt, and ground black pepper.
Pour this combined mixture over the chicken in the slow cooker, ensuring the meat is well covered.
Secure the lid and cook on the LOW setting for 6 to 8 hours. Cooking on HIGH is not recommended and untested for this recipe.
Roughly 30 to 40 minutes prior to serving, remove the chicken and shred it using two forks or your preferred method. Return the shredded chicken to the slow cooker and mix it in.
Approximately 20 to 30 minutes before serving time, bring a generously salted pot of water to a rolling boil. Cook the spaghetti noodles according to package instructions, drain them well, then incorporate them into the slow cooker.
Add the heavy whipping cream and sprinkle in the shredded white cheddar cheese. Stir until evenly distributed. Cover once again and allow it to rest for about 5 minutes to gently heat the cream and melt the cheese.
Uncover, garnish with freshly chopped parsley, and serve immediately while hot.