Mix the ground beef in a bowl with the salt and pepper. Form 4 patties.
Reserve 2 slices of the onion for the BBQ sauce.
Add the olive oil to a frying pan over medium heat. Add all but 2 slices of the onion (reserve those slices for the BBQ sauce) to the pan and saute over medium to medium-low heat until very soft, about 15 minutes.
Mix the mayonnaise with the garlic and refrigerate until you assemble the burgers.
In a saucepan over medium high heat, combine the BBQ sauce ingredients. Whisk together and bring to a boil. Reduce heat and simmer for 10-15 minutes, until reduced slightly and thickened. Remove from heat and set aside.
Preheat your grill to high heat. Grill the burgers for 2 minutes on each side. Then glaze the patties with the BBQ sauce and continue cooking for 2 more minutes per side for medium.
Add cheese after flipping for the final time.
Remove the patties from the grill and tent them with tinfoil to melt the cheese.
To assemble, toast the buns, then slather on the garlic mayo. Add the spring greens to the bottom bun, then the burger patty, then onions, then top with additional BBQ sauce.