Move oven rack to lower-middle position and preheat to 400°F. Season venison cubes with salt and roast for 3 to 4 minutes. Stir once or twice to ensure equal browning. Remove the meat and set aside and turn the oven down to 325°F.
In a large enameled Dutch oven, heat 3 tablespoons of oil over medium heat. Add chopped onion with a pinch of salt and cook until brown, stirring occasionally for about 10 minutes. Next, add tomato paste and garlic and stir for 1 minute. Sprinkle in flour and stir for 2 minutes. Then whisk in stock, ¾ cup Guinness, brown sugar, thyme, and rosemary, scraping the bottom of the pot to release browned bits. Simmer until slightly thickened, 2 to 3 minutes.
Add venison to the pot and bring back to simmer. Transfer the pot, uncovered, to the 325°F oven. Cook for 2 hours or until venison is almost tender—cooking time will vary. Stir halfway through cooking. Then add potatoes and carrots and continue cooking, covered this time, until vegetables and meat are tender, about 1 hour.
Before serving, discard thyme and rosemary sprigs and stir in remaining ½ cup of Guinness and chopped parsley. Season to taste with salt and pepper. Ladle into bread bowls.