Preheat oven to broil.
Arrange the serrano, banana, and jalapeno chile peppers on a baking sheet and place in the oven. Watch carefully and broil just until the skins blacken and blister, 4 to 5 minutes. Turn the peppers and continue broiling until all sides are blackened. Remove the peppers from the oven and place in a sealed paper bag to steam. After 15 to 20 minutes, remove peppers from the bag and peel off the crispy black skin. Remove stems and seeds from thepeppers, coarsely chop, and place in a bowl.
Heat the canola oil in a large skillet over medium heat until a pinch of flour sprinkled over the oil just begins to bubble. Whisk in the rest of the flour and cook, whisking continuously, until the mixture is well blended and dark brown, about 20 minutes. Once it becomes dark brown, remove the roux from the heat.
Place 2 tablespoons of canola oil into a deep soup pot and heat over medium-high heat. When the oil is just about to smoke, stir in the celery with half of the onions and bell peppers. Cook and stir until the vegetables are tender and the onion is transparent, about 5 minutes. Stir 1/4 cup of the vegetable broth into the pot. Cover, and simmer until almost all the liquid is evaporated, 10 to 15 minutes.
Stir the serrano, banana, and jalapeno chile peppers, along with the uncooked bell peppers and onions, garlic, Cajun seasoning, smoked paprika file powder, into the cooked bell peppers and onions. Stir the roux and 1 cup of stock into the vegetable mixture until the roux dissolves. Cover and simmer 5 minutes. Add the tomatoes, sweet potato, parsnip, red beans, black-eyed peas, okra, and remaining stock. Simmer uncovered 30 minutes more. Season to taste with salt and pepper.
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