Season the Wild Boar: Season the 1-inch wild boar cubes generously with salt and pepper, making sure the pieces are evenly coated.
Heat the Olive Oil: Place a large pot or Dutch oven over medium-high heat and add the olive oil, allowing it to heat before adding the meat.
Brown the Meat: Add the wild boar in batches so the pot is not overcrowded, then brown the pieces on all sides. Once browned, remove the meat from the pot and set it aside. Sauté the Vegetables: Add the chopped onion, minced garlic, diced carrots, and diced celery to the same pot. Sauté until the vegetables begin to soften.
Deglaze with Red Wine: Pour in the red wine and use a wooden spoon or spatula to scrape the browned bits from the bottom of the pot. Let the wine reduce by half.
Build the Stew: Return the browned wild boar to the pot, then add the beef or game stock, diced tomatoes, tomato paste, dried thyme, dried rosemary, and bay leaves. Add the chopped mushrooms or cubed potatoes at this stage if using. Bring to a Boil: Increase the heat as needed to bring the stew to a boil, allowing all the ingredients and cooking liquid to come together.
Simmer Until Tender: Reduce the heat to low, cover the pot, and let the stew simmer gently for about 2 to 3 hours, or until the wild boar is tender.
Remove the Bay Leaves: Take out the bay leaves before serving.
Adjust the Seasoning: Taste the stew and add more salt or pepper if needed, then serve while hot.