In a large pot or Dutch oven, heat a small amount of vegetable oil over medium-high heat.

Brown the beef, pork, and chicken in batches, adding more oil if needed. Transfer the browned meat to a plate.

In the same pot, add the chopped onion, garlic, celery, green bell pepper, and red bell pepper. If the pot is dry, add a bit more oil.

Sauté the vegetables until softened, about 5 minutes.

Return the browned meats to the pot.

Add the broth, bay leaves, thyme, basil, smoked paprika, Worcestershire sauce, hot sauce, salt, and pepper.

Bring to a boil, then reduce the heat to low. Cover and simmer for 1.5 to 2 hours, until the meats are tender and easily shredded.

Add the potatoes, carrots, shoe peg corn, lima beans, and okra (if using) to the pot.

Stir in the crushed tomatoes.

Simmer uncovered for an additional 45 minutes to 1 hour, until the vegetables are tender and the burgoo has thickened.

Remove the meats from the pot and shred them with two forks.

Return the shredded meat to the pot and stir to combine.

Ladle the burgoo into bowls and serve hot with cornbread or crusty bread.