Blend mayonnaise, sugar, pureed chipotle and lime juice together in a medium bowl. Cover and place in refrigerator for at least 30 minutes before serving.
Grill or broil turkey burgers, 4 inches from the heat, to an internal temperature of 165 degrees F.
Heat roasted onions and peppers on grill.
Split and grill rolls, cut side down, until golden brown.
Evenly spread 2 tablespoons chipotle mayonnaise on each roll.
About 30 seconds prior to removing turkey burgers from grill, top each with heated onions and peppers, then with cheese. Cover with lid to allow heat to melt cheese.
Place tomato slices and lettuce on the roll.
Place turkey burger on bottom of roll. Cover with roll top.