Fill a large pot with about a quart of water, cover and bring to a boil. Once boiling, add chicken breasts and simmer for 15-20 minutes or until meat is fully cooked (fully white inside, juices run clear).
In a small pot over medium-low heat, add beans, 2 tbsp barbecue sauce, tomato paste, garlic, and smoked paprika. Cover and cook for about 10 minutes, stirring occasionally. Add a tbsp of water if the beans begin to stick to the bottom of the pot.
While the chicken and beans are cooking, heat a large pan with olive oil over medium heat and add zucchini and salt and pepper. Sautee for 5-7 minutes until tender.
Heat the corn on the stovetop or microwave for 5-7 minutes until fully warmed through.
Once the chicken is fully cooked, you can shred it easily by placing it in a large bowl and using an electric hand mixer (if you do not have an electric mixer, use two forks to shred the chicken). Mix in the remaining barbecue sauce (about 1/3 cup).
Assemble the bowls by adding bbq chicken, beans, corn, and zucchini. Top with pickled onions if desired.