Place the first 6 ingredients in a bowl and mix until just combined. Shape into 4 patties each about 3/4” thick, set on plate and set aside for moment.
Preheat your barbecue or indoor grill to medium-high. Grill the vegetables as per package direction, and then set transfer to plate.
Now cook the burgers for about 4 minutes per side, or until entirely cooked through and the centre of the burger reaches 160 degrees F (71 degrees C) on an instant read meat thermometer.
While the burgers cook, use kitchen scissors to cut each piece of grilled vegetable into two or three pieces, making them a better size to sandwich into a burger.
When cooked, top burgers with the cheese and the grilled vegetables. (You may not need all the vegetables, but save and refrigerate and eat the next day.) Turn the heat to low, close the lid and cook 1 to 2 minutes more, or until cheese is melted.
Spread buns with the mayonnaise. Top the bottom buns with a lettuce leaf. Set on the burgers, top buns and serve.
Recipe Options: Instead of bison, use lean ground beef or lamb in this recipe.