Heat the olive oil in a skillet over medium-high heat. Cook and stir until browned and no longer pink. Stir in the onion soup mix, ketchup, sherry, Worcestershire sauce, garlic, and black pepper. Bring to a simmer, then reduce heat and simmer uncovered 15 minutes.
While the venison is simmering, butter the hamburger buns, and toast on a skillet over medium heat. Set aside.
Spoon the venison mixture onto the toasted buns. Serve open faced sprinkled with Muenster cheese and red onion rings.