Sear the Venison: Pat the venison cubes dry with paper towels. Season generously with salt and pepper. Heat the olive oil or bacon grease in a large Dutch oven or heavy-bottomed pot over medium-high heat. Working in batches, sear the venison on all sides until nicely browned. This step is crucial for developing deep flavor. Remove the venison and set aside.
Sauté the Aromatics: Add the chopped onion to the pot and cook until softened and translucent, about 5-7 minutes. Add the carrots and celery and cook for another 5 minutes, stirring occasionally. Stir in the minced garlic and cook for 1 minute more until fragrant.
Build the Flavor Base: Stir in the dried thyme, dried rosemary, and smoked paprika. Cook for 30 seconds, stirring constantly, until fragrant. Add the tomato paste and cook for another minute, stirring to coat the vegetables.
Deglaze (Optional): If using red wine, pour it into the pot and scrape up any browned bits from the bottom. Let it simmer for a few minutes, allowing the alcohol to cook off and the flavors to meld.
Bring it Together: Return the seared venison to the pot. Add the beef broth, Worcestershire sauce, and bay leaf. The liquid should mostly cover the meat and vegetables; add a little more broth if needed.
Simmer Low and Slow: Bring the stew to a gentle simmer, then reduce the heat to low, cover the pot, and let it cook for at least 2 hours, or up to 3 hours, until the venison is fork-tender. The longer it simmers, the more the flavors will meld and deepen.
Add the Potatoes: During the last 45 minutes to an hour of cooking, add the chopped potatoes to the stew. They should be tender when the venison is ready.
Thicken (Optional): If you prefer a thicker stew, whisk the all-purpose flour with a few tablespoons of cold water in a small bowl until smooth. Gradually stir this slurry into the simmering stew and cook for another 5-10 minutes, or until the stew has thickened to your desired consistency.
Season and Serve: Remove the bay leaf. Taste the stew and adjust the seasoning with salt and freshly ground black pepper as needed. Ladle the stew into bowls and garnish with fresh chopped parsley.