How to Make It
In a sturdy plastic bag, combine the cornmeal with salt and pepper. Add the chicken in batches and shake to coat.
In a large heavy casserole, heat the oil until shimmering. Add the chicken and fry over moderately high heat, turning once, until well-browned, about 12 minutes; reduce the heat if the chicken browns too quickly. Transfer the chicken to a large platter.
Pour off all but 2 tablespoons of the fat in the casserole. Add the onions and jalapeño and cook over low heat until just softened, about 3 minutes. Add the water, vinegar, peanuts and garlic, season with salt and pepper and bring to a simmer. Return the chicken to the casserole, cover and simmer over low heat until tender and cooked through, about 45 minutes. Transfer the chicken to a platter.
Add the sweet potato, eggplants and yellow squash to the casserole. Cover and cook over low heat until the vegetables are very tender, about 1 hour. Return the chicken to the casserole, add the scallions and simmer until the scallions are tender and the chicken is hot, 10 to 15 minutes. Season with salt and pepper and serve.