Heat the oil in a large heavy pot over medium heat. Add the pork and beef in batches, browning on all sides. Remove and set aside. This step builds the base flavour of the stew.
Add the chicken thighs to the same pot and sear for 3 to 4 minutes per side. Remove and set aside with the other meats. The browned bits left behind will enrich the broth.
In the same pot, add the onion, bell pepper, celery, and carrot. Cook for 6 to 8 minutes until softened. Stir in the garlic and cook for another minute until fragrant.
Return all the meats to the pot. Pour in the chicken stock and add the bay leaf, thyme, paprika, Worcestershire sauce, and vinegar. Bring to a boil, then reduce to a gentle simmer.
Cover and simmer for 1 hour, skimming off any foam. This slow cooking allows the meats to tenderise and the flavours to deepen.
Stir in the potatoes, tomatoes, corn, and green beans. Season with salt and pepper. Simmer uncovered for another 45 minutes, stirring occasionally to prevent sticking.
Remove the chicken thighs, discard the bones and skin, and shred the meat. Return the shredded chicken to the pot and stir through.
If the stew is too thin, mash a few potatoes against the side of the pot to thicken. If too thick, add a splash of water or stock. Simmer for 10 more minutes.
Turn off the heat and let the stew rest for 10 minutes. This helps the flavours settle and the texture to even out before serving.
Ladle into bowls and serve hot with cornbread or saltine crackers. Offer hot sauce on the side for those who like a bit of heat. Garnish with chopped parsley if desired.