Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high.
For the patties: Combine the chuck, sirloin, jerk seasoning, wine, and salt in a large bowl. Mix lightly and form into 6 patties. Refrigerate until ready to grill.
For the sauce: Mash the avocado with the lime juice in a bowl. Stir in the mayonnaise and salt. Gently fold in the mint leaves. Cover and refrigerate until ready to serve.
For the glaze: Combine the wine, vinegar, honey, chiles, and salt in a fire-proof saucepan. Place on the grill rack and cook, stirring often, until the mixture is reduced by half.
When the grill is ready, brush the grill rack with the oil. Place the patties on the rack over direct heat. Cook for 4 to 5 minutes per side, basting often with the glaze until the desired doneness is reached.
Brush some of the glaze on the cut sides of the rolls. Place the rolls, cut side down, on the rack and grill until lightly toasted. Remove the rolls and place on a serving plate.
To assemble the burgers, place a lettuce leaf on each roll bottom. Top with a tomato slice. Add a patty, a dollop of the sauce, and a roll top.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.