Bring a pot of water to a boil with 1 quarter piece onion and 1 tablespoon bouillon. Add chicken and boil until chicken is no longer pink in the center and juices run clear, 30 to 40 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C). Remove chicken and set aside on a plate. Reserve 1 cup cooking water.
Combine Mexican crema, chipotle peppers, reserved 1 cup cooking water, 2 tomatoes, 1 quarter onion, 1 garlic clove, and remaining 1 tablespoon bouillon in a food processor. Blend sauce well until smooth.
Transfer sauce to a frying pan and add chicken thighs. Bring to a simmer and let cook for 20 minutes.
Meanwhile, heat 1 tablespoon butter over medium heat in a skillet. Add 1 quarter onion and remaining garlic clove. Cook and stir until softened, 3 to 4 minutes. Add bell pepper and cook and stir until softened, about 3 minutes. Stir in squash. Season with salt and pepper and saute until squash is cooked through and tender, about 5 minutes.
Slice remaining tomato. Heat remaining tablespoon butter in a skillet over medium heat. Add tomato and remaining 1 quarter onion. Cook and stir until softened, 3 to 4 minutes. Place on top of chicken mixture and serve with squash.