- Place the 1 Tbsp. oil in a non-stick skillet set over medium heat. Add the onions and cook until tender, about 5 minutes. Remove onions from the heat and set aside.
- Divide and shape the ground beef into 4, 3/4” thick patties. Brush the patties with the 2 Tbsp. olive oil; season with salt and pepper.
- Heat your barbecue to medium-high. Place the wood chips in your smoker box, or fold and seal inside an 18” x 12” piece of tinfoil. If using foil, poke the packet with a fork several times to allow smoke to escape.
- Set the wood chips directly on the coals (just above the gas burner) on one side of the barbecue and close the lid. When the chips really start smoke, quickly set the hamburger patties on the grill directly above the wood chips. Close the lid and turn heat under the patties to medium-low; leave the other side of the barbecue set to medium-high. Cook and smoke burgers 4 minutes. Turn the patties over, and cook and smoke 4 minutes more. Spoon some barbecue sauce on each patty; divide and top with cheese. Cover and cook about 2 to 3 minutes more, until the cheese is melted and the centre of each burger reaches 160 degrees F (71 degrees C) or above on an instant read meat thermometre.
- Spread the buns with mayonnaise. Set a lettuce leaf on each bottom bun. Set on the burgers. Top with onions and top buns. Serve with pickles, if desired.
Note: Wood chips for smoking are available in bags at most stores selling barbecuing equipment. In this recipe, they are not presoaked as is often done. You want to quickly generate a lot smoke to flavour the burgers, and having them dry will achieve that.