Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Season the ground buffalo with pepper; form into 8 balls. Press a cavity in each ball with your thumb pressing halfway into each ball; place a tablespoon of your cheese into the hole and seal the meat around the cheese. Press each ball into a patty shape.
Cook the burgers on the preheated grill until cooked to your desired degree of doneness, 4 to 6 minutes per side for well done. An instant-read thermometer inserted into the center should read 160 degrees F (70 degrees C). Spread the toasted buns with mayonnaise. Place a burger patty onto each bun bottom, then place a lettuce leaf, onion rings, and tomato slice onto each sandwich. Top with the remaining buns to serve.