Thoroughly clean the beef tripe under cold running water, removing any excess fat. Cut the tripe into 2-inch squares and place in a large stockpot. Cover with water and bring to a boil, then drain and rinse. This blanching step removes impurities.

Return the cleaned tripe to the stockpot and add 12 cups of water. Bring to a boil over high heat, then reduce to a gentle simmer. Skim off any foam that rises to the surface. Cover and simmer for 2 hours until the tripe begins to soften.

While the tripe simmers, prepare the vegetables. Dice the onions and bell peppers. Mince the garlic cloves. Chop the tomatoes into chunks. Peel and cut the carrots into rounds. Peel and cube the potatoes into 1-inch pieces.

Heat olive oil in a large skillet over medium heat. Sauté the onions until translucent, about 5 minutes. Add the bell peppers and garlic, cooking for another 3 minutes until fragrant. Add the tomatoes and cook until they break down, about 8 minutes.

Add the sautéed vegetable mixture to the pot with the tripe. Season with salt, black pepper, cumin, and oregano. Add the bay leaves. Stir well to combine all ingredients.

Add the carrots to the pot and continue simmering for 30 minutes. Then add the potatoes and cook for an additional 30 minutes until all vegetables are tender and the tripe is completely soft.

Taste and adjust seasoning as needed. Remove the bay leaves. Stir in fresh cilantro just before serving. Ladle the hot soup into deep bowls and serve with lime wedges and warm tortillas on the side.