Combine all the ingredients for the patties in a large mixing bowl and mix together really well using your hands. Cover the mixture and chill for at least 30 minutes. When ready to cook the burgers, remove the patty mixture from the fridge and allow to stand for 10 minutes. Pre-heat the grill to hot. Divide the patty mixture into 4 large balls and shape into patties. Arrange on a lined baking tray and grill for 12-15 minutes, turning occasionally until golden brown on both sides and cooked through in the middle. Spread the bottom halves of the burger buns with the tomato ketchup, then arrange a few white onion rings on top. Remove the patties from the grill and pat dry. Top with the slices basil, then arrange on serving boards with the other half of the bun to one side. Garnish with a little of the shallot before serving.
