Brown the venison: Heat the olive oil in a large, heavy-based pot or Dutch oven over medium-high heat. Add the venison chunks in batches, making sure not to overcrowd the pot. Brown the meat on all sides, which should take about 5-7 minutes per batch. Once browned, remove the venison and set it aside.
Sauté the vegetables: In the same pot, add the chopped onion, carrots, and celery. Cook over medium heat, stirring occasionally, until the vegetables begin to soften, about 5 minutes. Add the garlic and cook for another minute, until fragrant.
Add the tomato paste: Stir in the tomato paste and cook for 2-3 minutes, allowing it to caramelise slightly and deepen in flavour.
Deglaze with red wine: Pour in the red wine, scraping up any browned bits from the bottom of the pot with a wooden spoon. Bring the wine to a simmer and cook for 5-7 minutes, allowing it to reduce slightly and concentrate in flavour.
Add the stock and seasonings: Return the browned venison to the pot, followed by the beef stock (or game stock), thyme, bay leaves, and black peppercorns. Stir to combine. Bring the mixture to a boil, then reduce the heat to low and cover the pot.
Simmer the stew: Let the stew simmer gently on low heat for about 2 to 2.5 hours, or until the venison is tender and the flavours have melded together. Stir occasionally, and check that the stew doesn’t dry out; if it does, add a little more stock or water to keep the meat submerged.
Finish the stew: Once the venison is tender, taste and adjust the seasoning with salt and pepper as needed. If desired, add 2 tablespoons of butter to the stew for extra richness and to smooth out the sauce.
Serve: Ladle the ragoût into bowls, garnish with fresh chopped parsley, and serve hot. This dish is traditionally enjoyed with mashed potatoes, crusty bread, or a side of roasted root vegetables.