In a medium bowl, combine the ground beef with Worcestershire, parsley, thyme, garlic salt, and pepper.
Form into 4 patties.
Cover and set in refrigerator until ready to cook, at least one hour.
Heat 1 tbs olive oil in a large ovenproof skillet over medium heat. Add the onion and cook for 8-10 minutes until just starting to brown.
Add the wine, scraping up any browned bits, cover, reduce heat to low and cook for 10 – 15 minutes more.
Remove from skillet, cover with aluminum foil, and set aside.
Wipe out the skillet, increase heat to medium-high. Add 1 tbsp oil and heat until just smoking. You want the skillet hot.
Sprinkle a dash of salt on the top and bottom of every patty and place in the skillet without over overcrowding your skillet. Cook until a nice crust forms on bottom, about 4 minutes.
Flip and cook 4 to 5 minutes longer. Remove skillet from heat.
Place slices of cheese on burgers and place skillet (if oven safe) under the broiler until cheese is golden and melty, about 1 minute.
Mix the mustard and mayo together and spread on toasted buns. Top with a patty and a heaping portion of onion.