Prepare the sauce by adding mayonnaise, ketchup, relish, vinegar, salt and pepper to a small bowl and mixing until thoroughly combined.
Heat olive oil and brown sugar over medium heat in a saucepan.
Add onion and cook for 10-12 minutes until caramelized, stirring frequently. Set aside.
In a medium mixing bowl, add ground beef, pepper and salt. Mix until thoroughly combined.
Divide into 4 equal portions, rolling and compacting with hands before flattening into ½-⅓ inch patties.
Over medium heat, lightly coat a skillet with non-stick cooking spray and add patties.
Using a spoon, spread a tablespoon of yellow mustard over the top of each burger.
Cover with a lid and cook on medium heat for 3-4 minutes until browned, flip and cook another 3-4 minutes. Burgers should reach 160°F internally.
Once burgers are done, remove from heat and place them on a plate. Allow to cool slightly then top each burger with a slice of cheese.
Lightly toast the buns by placing them face down in a skillet over medium heat for 2-3 minutes.
Assemble the burgers by adding a teaspoon of sauce to the bottom buns. Next add lettuce, tomato, patty, caramelized onions, additional sauce and top bun.