Peel and slice onions into thin slices.
Melt 2 tablespoons butter in a large heavy bottomed skillet over medium-low heat.
Add onions and thyme to the skillet. Stir to coat onions with the butter.
Cook onions over medium-low heat, stirring often until onions begin to brown.
After about 10 minutes, add a couple tablespoons water to prevent onions from sticking and burning.
Continue cooking onions, adding water when mixture seems dry, until onions turn a deep golden brown.
When onions are caramelized to a deep golden brown, add a tablespoon of balsamic vinegar.
Continue cooking for another 2-3 minutes until liquid has cooked off.
Season with salt to taste.
Remove from heat. Set aside.
Place ground beef in a mixing bowl.
Add soup mix and Worcestershire sauce to the beef.
Mix together and form beef into four patties.
Spread mayonnaise onto the hamburger buns.
Heat barbecue grill to 350°.
Grill beef patties, 7-8 minutes per side or until cooked through.
Top each patty with a slice pf provolone cheese and a mound of grilled onions.
Grill each bun until toasted.
Place a slice of Provolone cheese on each bottom portion of the grilled bun.
Top with a beef patty and the top half of the buns.
Serve immediately.