Step 1

Heat oil in a large skillet over medium-high heat until shimmering. Add onions and peppers and cook, stirring frequently, until softened and browned in spots, about 8 minutes. Add vinegar and sugar. Remove from heat and stir until sugar is dissolved. Season to taste with salt and pepper.

Step 2

Light 1 chimney full of charcoal. When all charcoal is lit and covered with gray ash, pour out and arrange coals on one side of charcoal grate. Set cooking grate in place, cover grill, and allow to preheat for 5 minutes. Alternatively, set half the burners on a gas grill to the highest heat setting, cover, and preheat for 10 minutes. Clean and oil grilling grate.

Step 3

Transfer onion and pepper mixture to a 10-inch-square disposable aluminum pan. (Alternatively, construct a tray out of a double layer of heavy-duty aluminum foil, 10 inches square, with sides about 2 inches high.) Nestle sausages into onion and pepper mixture.

Step 4

Place tray on hot side of grill and cook until simmering, about 4 minutes. Slide to cooler side of grill. Cover grill, with vents over sausages. Cook with all vents open until sausages register 140 to 145°F (60 to 63°C) on an instant-read thermometer, about 20 minutes, turning once halfway through.

Step 5

Remove lid. Using tongs, remove sausages from peppers and place directly on cooking grate over hot side of grill. Cook, turning occasionally, until well browned and crisp, about 3 minutes total. Return sausages to peppers. Toast buns over hot side of grill, if desired. Serve sausages with buns and sweet-and-sour peppers.