Remove the mince from the fridge 30 mins before cooking to reach room temperature. Put the mince in a bowl and mix in 1 tsp sea salt, pepper, the grated onion and Worcestershire sauce. Mix well with your (clean) hands, then divide into 4 equal-size balls. Wrap a basil leaf around each slice of brie and press into the middle along with the tomato and re-shape the meat to a flat patty, 11⁄2cm thick.
Heat the grill for 5 mins. Fit the grill rack to its highest level. Lay the burgers evenly over the rack so they are under the hottest parts of the grill. Brush with oil from the sundried tomatoes and season.
Grill the first side 3 mins for medium-rare or 5 mins for well done. Brush the other side with oil, season and grill for the same length of time. Allow to stand for 3 mins before serving. Pack into a crusty bun with salad leaves, cornichons, tomatoes and relish.