Divide the beef mince into 4 relatively equal portions. Press each portion into a patty slightly larger in diameter than the buns. Press the centre portion of the patties slightly thinner than the edges (burgers tend to “dome up” when grilled, and doing this results in a flatter top).
Lightly oil the barbecue plate and preheat to high
To make the chill sauce, place 2 teaspoons of oil in a frying pan and heat over medium high heat. When the oil is hot, add the green chillies and red onion. Stir frequently until the onion has softened, about 2 minutes. Add the salt and garlic and stir until fragrant, about 30 seconds. Remove the pan from the heat, but keep it warm.
When the BBQ is hot, place the patties on the plate, concave side down. Cook for 3-5 minutes, depending on how well-done you like them, then turn them over to cook the other side.
Open the buns and put them on the grate to toast. Barbecue the patties on the flipped side for 2 minutes (or more if you want), then top each patty with the chilli mixture and a slice of cheese. Continue to cook for a minute or two to allow the cheese to melt (close the lid on your barby if you have one). Place the patties in the buns and serve hot.
Steps 1 and 3 may both be done ahead of time and the patties and topping stored in the refrigerator for up to 24 hours. Allow the patties to come back to room temperature for 30-45 minutes before barbecuing and re-heat the topping in a pan before putting it on the patties.