Combine all the ingredients for the quick pickles and let sit on the counter at room temperature while preparing the spicy mayo and burgers. Combine the spicy mayo ingredients, stirring well, and refrigerate until serving time.
Combine the ground beef with ¼ cup Korean BBQ Sauce and the green onions. Divide into 4 equal portions and form into patties making an indentation in the center of each patty.
Heat a grill pan or skillet over medium-high heat. Spray with cooking spray then add the patties to the pan. Cook for 3-4 minutes or until a crust has formed on the bottom. Reduce the heat to medium, flip the burgers and cook for another 3-4 minutes for medium, longer if you like your burgers more well done.
Serve the burgers with the buns, lettuce leaves, quick pickles, and spicy mayo.