In a large bowl, mix together the onion, garlic, red chilli and beef mince until well combined. Gradually pour in the beaten egg and mix well. Season, to taste, with salt and freshly ground black pepper.
Divide the mixture equally into four. Using wet hands, roll the mixture into balls the size of a tennis ball. Using the palms of your hands, flatten the balls slightly into patties about 3cm/1¼in thick. (NB: Make sure all the burgers are the same thickness so that they cook evenly.)
Place the patties onto a plate, cover with cling film and chill in the fridge for 30 minutes to one hour.
Heat the barbecue until hot. Lightly brush one side of each patty with oil and place, oiled-side down, onto the grill. Cook for 4-5 minutes, or until golden-brown. (NB: avoid moving the burgers on the grill or they may stick).
Lightly brush the other side of the burgers with oil, then turn over, using tongs, and cook for a further 4-5 minutes, or until the burgers are browned and completely cooked through.
Transfer the burgers to a plate and set aside for 5-10 minutes, to rest.
Slice each burger bun in half and grill, cut-side down, on the barbecue grill. Toast for 1-2 minutes, or until pale golden-brown.
To serve, place one burger inside each toasted burger bun. Top with your choice of accompaniment.