Preheat the oven to 325 degrees. Season the roast well with salt and pepper. Use a large Dutch oven with a lid. Add 2 tablespoons of oil, and heat over medium. When the oil shimmers, add the seasoned roast and cook until browned, 8 to 10 minutes per side. Transfer the roast to a platter to hold.
Brown the seasoned roast well on all sides.
Add the remaining 2 tablespoons of oil to the pan. Add the onions and season them well with salt. Cook over medium heat, stirring often, until the onions are golden-brown and soft, about 10 minutes. Add the garlic and cook for an additional 5 minutes. Stir in the paprika and cumin and cook for 1 minute. Add the fire-roasted tomatoes and brown sugar and cook, stirring, for 5 minutes. Stir in the coffee and chicken broth. Bring the mixture to a simmer.
Add the coffee, stock, tomatoes and seasonings to the browned onions.
Return the venison roast to the pan. Place the lid on the pot and transfer it to the oven. Roast until the venison pulls apart easily, 3 1/2 to 4 hours.
Slow cook the roast until it just about falls apart.
Transfer the roast to a cutting board and let cool for 20 minutes. Skim any fat from the braising liquid. Add the cornstarch and water mixture, and bring to a boil over medium heat to thicken the gravy. Check for seasoning and add salt and pepper as needed. Add the butter and stir it into the gravy as it melts. Use a pair of forks to shred the venison roast.
Use forks to shred the roast.
Return the meat to the gravy to warm through.
Return the shredded meat to the thickened gravy to heat through.