Bring a large pot of heavily salted water to a boil. Add the spaghetti and cook for about 10 minutes, until just shy of al dente. Reserve ½ cup pasta water, then drain and toss with 1 tablespoon olive oil. Set aside.
Preheat the oven to 350°F. Lightly spray a 13×9-inch baking dish with nonstick spray and set aside.
Heat the remaining tablespoon of olive oil in a large Dutch oven over medium-high heat. Add onion and bell pepper with a pinch of salt and pepper. Sauté for about 5 minutes until soft and translucent.
Add diced tomatoes with green chilies and cook for about 5 minutes, until most of the liquid evaporates.
Stir in the cream of mushroom soup, cream of chicken soup, and chicken stock. Bring the mixture to a simmer.
Add cheddar cheese and Velveeta, stirring until melted and smooth. Stir in the cooked chicken and season with salt and pepper to taste.
Mix the cooked spaghetti into the sauce. Add some reserved pasta water if needed to loosen the mixture.
Pour the mixture into the prepared baking dish and spread evenly.
Bake for 30–40 minutes, until the sauce is bubbly and the top turns golden.
Serve hot and enjoy.