Place all of the brine ingredients in a large pot and bring to a simmer. Stir until the salt and sugar have dissolved. Remove the brine from the heat, let come to room temperature and then place in the refrigerator to thoroughly chill.
Place the venison into the brine and put a plate on top to keep the meat fully submerged. Place in the refrigerator and brine for 3 to 5 days.
Remove the venison from the brine, rinse under cold water.
Place the meat into a large pot and cover with water. Be sure not to overfill, as the pot can overflow while cooking.
Bring to a boil and then reduce to a simmer. Cover and cook at a low simmer until the meat is fork tender. This can take between 3 and 5 hours depending on which cut you are using. Make sure that the water level is above then venison during the cooking process. If it becomes low, add what's needed to cover the meat.
For the juiciest product, let the venison cool to room temperature in the cooking liquid and place it in the refrigerator overnight. The next day, warm on the stovetop until just heated through.