Keeping the oil to one side, mix the rest of the patty ingredients together in a large bowl, adding just enough egg to bind the mixture. Reserving some of the meat to make toddler-size balls, divide the rest into 4 adult-size balls and flatten into patties. Put on a plate and leave in the fridge to firm up for at least a couple of hours, or overnight.
Heat a grill or griddle pan to a medium heat. Rub a little oil over the burgers and grill or fry them for 8 minutes on each side.
Meanwhile, toast the seeded rolls on the cut sides and then spread a little mayonnaise over the bottom sides and top with lettuce and tomato.
Place the burgers on top, then add onion, avocado and relish.