Stuffed French Onion Soup Burger

Name: Stuffed French Onion Soup Burger
Ingredients: 3 large red onions, cut into 1/2-inch rounds; 2 large cloves garlic, thinly sliced; 6 tablespoons canola oil; Kosher salt; 2 tablespoons dry Marsala; 1 tablespoon dark brown sugar; 1 tablespoon Dijon mustard; 1 tablespoon red wine vinegar; 1 1/2 pounds hamburger meat (85/15); Kosher salt and freshly ground black pepper; 2 tablespoons low-sodium soy sauce; 1 tablespoon Worcestershire sauce; 3 cups grated Gruyere; 2 cups hearty beef stock; 4 seeded potato hamburger rolls; 8 to 12 thick sour pickle rounds