Mix meat, salt, pepper and tabasco with hands and set aside.
Preheat grill on medium. Put 2tbsp of butter in a medium pan and place on stove at low heat. Add onions and brown sugar. Toss to combine and let set on low heat for 20 minutes or until onions are caramelized and light brown.
Meanwhile combine mayo, dijon and lemon juice in small bowl. Set aside.
Grab buns and butter inside of each slice. Place on preheated grill and toast until there are char marks. Let buns cool.
While buns are cooling form 2 patties out of the beef. Place both patties on grill and cook for 3 minutes, rotating about 45 degrees and continue to cook for a minute. Flip burgers, cook for 2 minutes, rotate 45 degrees again and top with a cheese slice and onions. Close grill lid and allow to cook for another minute. Take off of grill and let sit for a minute or so.
While burgers set smear mayo mixture on inside bottom buns and top with a handful of arugula. Place burgers on top and serve with the other toasted bun. Get ready for some happy burger lovers!
Recipe by pretty plain janes at https://prettyplainjanes.com/2015/05/28/onion-gruyere-and-arugula-burgers/