Prepare the grill for direct cooking over medium heat (350° to 450°F).
Brush the cooking grates clean. Grill the bell peppers and jalapeño over direct medium heat, with the lid closed, until blackened and blistered all over, 12 to 15 minutes, turning occasionally. Put the peppers in a bowl and cover with plastic wrap to trap the steam. Let stand for about 10 minutes. Peel away and discard the charred skin, stems, and seeds. Coarsely chop and place in a food processor. Add the remaining sauce ingredients and process until the sauce is blended but still slightly chunky. Transfer to a bowl.
In a small bowl whisk the mayo ingredients.
Mix the patty ingredients, and then gently form four patties of equal size, each about ¾ inch thick. With your thumb or the back of a spoon, make a shallow indentation about 1 inch wide in the center of each patty to prevent them from forming a dome as they cook. Refrigerate the patties until ready to grill.
Brush the cooking grates clean. Grill the patties over direct medium heat, with the lid closed, until cooked to medium doneness (160°F), 7 to 9 minutes, turning once. During the last 30 seconds to 1 minute of grilling time, toast the rolls, cut side down, over direct heat.
Build each burger on a roll with the mayo mixture, a patty, roasted chile sauce, onion, and mint. Serve immediately.