Preheat a barbecue or grill to medium-high. Cook the burgers for 12-15 minutes, turning occasionally, until cooked to your liking.
Meanwhile, heat the oil in a frying pan. Add the red onion and cook over a low heat for 10-15 minutes, stirring occasionally, until softened and starting to caramelise.
Slice the rolls in half and toast cut-side down on the barbecue, or place cut-side up under the grill, for 1 minute until lightly toasted.
Put the burgers on the grilled bun bases and top each with a slice of brie, the caramelised red onions and a few salad leaves.