Heat the olive oil in a stock pot over medium heat; add the onion and cover. Cook the onions until soft and translucent, about 5 minutes. Stir the squash, great Northern beans, and lima beans into the pot; pour the chicken stock over the mixture. Cover and cook until the squash is tender and beginning to break apart, 30 to 45 minutes. Stir the corn and basil into the stew; cook until the stew reaches the consistency of pancake batter, about 10 minutes more. Sprinkle the chopped banana pepper over individual portions to serve.