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Step 1
Pour the oil into a large Dutch oven or soup pot and set the heat to medium-high. Working in batches, brown all the meats. Do not crowd the pan or the meat will not brown well. Salt the meat as it cooks. As they brown, move the various meats to a bowl.
Step 2
Add the onions, carrots, celery and green pepper to the pot and turn the heat to high. Cook the vegetables until they are well browned; you might need to add a little more oil to the pot. When the vegetables have browned, add the garlic and cook for 1 minute. Add back the meats, along with the chicken and beef broths and the tomatoes. Stir to combine and add salt to taste. Bring to a simmer, cover, reduce the heat and simmer gently for 2 hours.
Step 3
Fish out the meat pieces. Strip the pheasant and squirrel off the bone. Tear the large pieces of venison into bite-sized pieces. The reason you did not do this right at the start is because venison will stay moister when it cooks in larger pieces. Return all the meat to the pot and return the stew to simmer.
Step 4
Peel and cut the potatoes into chunks about the same size as the meat pieces. Add them to the stew and simmer until they are tender. Add the Worcestershire sauce, mix well and taste for salt. Add more Worcestershire sauce to taste if needed.
Step 5
Finally, add the corn and lima beans. Mix well and cook for at least 10 minutes, or longer if you’d like. Serve with cornbread and a bottle of hot sauce on the side.