Preheat the oven to 350℉ (180℃).
Season chicken with salt, pepper, and Creole seasoning or your favorite spice mix.
Heat a Dutch oven or medium pan over medium-high heat with about a tablespoon of oil.
Then add the chicken and sauté for 5-6 minutes on each side until it's almost cooked through. Remove and set aside.
Add more oil (or butter) to the same pan if needed, then add the onions, garlic, thyme, and more Creole seasoning. Stir for 3-4 minutes, or until the onions wilt.
Cook the spaghetti in a large pot per the instructions, drain, and set aside while you make the sauce.
Toss in the tomatoes and bell peppers, and continue cooking for 2-3 minutes.
Stir in the flour until fully incorporated, about a minute. Gradually stir in the evaporated milk and broth. Bring to a boil, stirring constantly for about 2 minutes or until the sauce thickens and bubbles.
Stir in all but about ½ cup of the cheeses (reserve the rest for the top), and continue stirring until everything's melted, evenly combined, and smooth. Adjust seasonings with salt, pepper, and Creole seasoning.
Add the chicken and spaghetti to the sauce, and stir gently to evenly coat.
Transfer the mixture to a lightly greased lasagna pan or 4-quart baking dish, and top with the remaining cheese.
Bake at 350℉ (180℃) for 20 minutes or until golden and bubbly.