In a large pot, heat 2 tablespoons olive oil over medium-high heat. Season the venison with salt and black pepper. When the oil shimmers, add the venison. Sear on all sides until nicely browned.
Pour in enough venison stock or beef broth to just cover the meat. Cover and simmer until tender, about 3 to 4 hours. Check the liquid periodically and add more stock as needed to keep the meat covered.
When the meat is fork tender, remove it from the pot. Reserve 4 cups of the cooking liquid for Step 5. Shred the venison and set aside.
Heat a clean pot over medium heat with the remaining 1 tablespoon olive oil. Add the onion and cook 5 to 6 minutes until translucent. Add the garlic and cook 2 minutes, stirring to prevent burning.
Add the reserved cooking liquid, soy sauce, white wine or sherry, cider vinegar, thyme, rosemary, bay leaves, carrots, and potatoes. Bring to a gentle simmer and cook until the potatoes are almost fork tender, about 12 minutes.
Add the shredded venison and sugar. Simmer 5 to 10 minutes, until the potatoes are tender and the broth tastes balanced.
Turn off the heat and fold in the cooked noodles, if using. Cover briefly to warm the noodles through.
Season to taste with salt and black pepper. Garnish with sliced green onions.