Make the sauce:
Mix the first 5 ingredients. Season with salt and pepper.
Make the onions:
In a skillet, heat the EVOO over medium heat. Add the onions and season with salt and pepper. Cook until browned, about 15 minutes. Stir in the stock (or consomme) and cook until tender, 10 to 15 minutes.
Make the burgers:
Combine the beef, worcestershire, garlic and parsley; season with coarse salt and pepper. Form into 8 thin patties and drizzle with EVOO. Top each patty with 1 tbsp. mustard. Preheat a large griddle pan over medium-high heat. Add the patties mustard side up and cook for 4 minutes. Flip and cook for 2 more minutes. Top with the cheese to melt in the last minute of cooking.
Stack 2 patties with some onions between them on each bun bottom. Top with the pickles, tomatoes, lettuce, special sauce and bun tops.