Preheat the air fryer to 375 degrees F (oven method, please see below).
Cut tomatoes and bell peppers into large chunks.
Toss the vegetables, peppers, and tomatoes with olive oil, salt, pepper, and creole seasoning (if not available, add garlic and onion powder instead).
Add the veggies on a baking sheet and roast in the air-fryer for 18-22 minutes or until tender and slightly charred.
While the vegetables are roasting, chop the onion, garlic, and basil.
In a pan, add oil and saute onion and garlic for a few minutes until aromatic. Add the basil, finish sauteeing for another minute, and remove from heat.
Once the vegetables are roasted, transfer roasted vegetables, sauteed onion, garlic, basil, and vegetable broth to a blender or food processor. Blend or process until smooth (be your judgment, and blend to your liking).
In a saucepan, make the roux by melting the butter and then the flour. Cook the roux, whisking constantly, for 2-3 minutes or until it is light brown in color; do not burn it. (roux is optional)
Add the tomato and pepper soup mixture to the roux and mix.
If using heavy cream, add to the saucepan and bring the soup to a complete boil. If not using heavy cream, skip and bring the soup to a boil.
Taste and adjust to your liking. (Add salt or other seasoning if needed. If it is too salty, add a little bit more broth or heavy cream).
Serve hot, garnished with more heavy cream, basil, and a grilled cheese sandwich.