Season the chicken on both sides with a tablespoon of salt and 1½ tablespoon of pepper. Preheat a Dutch oven or other large, heavy pot over medium-high heat.
Add ½ cup of oil to the pot. Add half the chicken and fry it, turning once, until golden brown on both sides, about 10 minutes total, and transfer to a plate. Repeat with the remaining chicken, or you can place all the chicken in the pot as I did and let it brown for about 10 minutes.
Blend the onions, parsley, celery, tomato, and garlic in a food processor or blender into a fine paste. Pour all the mixture into the pot, scraping up any browned bits with a wooden spoon. Add Maggie or chicken bouillon, occasionally stirring, for 8-10 minutes. Add about ½ a cup of water if needed.
Mix the carrots and green beans into the pot of chicken; let it simmer for 2 to 3 minutes. Finally, add the green peppers, stir and let them blend, turn off the stove.
Using a sharp knife, cut both ends off the plantain. This will make it easy to grab the plantain skin. Slit a shallow line down the long seam of the plantain only as deep as the peel. Remove plantain peel by pulling it back.
Cut plantains into rounds about an inch thick.
Heat a large skillet or cast iron with oil up to ½ inch deep on medium-high heat until hot but not smoking.
Fry the plantains until golden brown, then toss them with the chicken and vegetable medley. But hold off on this until you are ready to serve the meal.
Serve immediately.