Melt 2 tablespoons butter in a medium size skillet over medium heat. Add the onions and season with salt, pepper and thyme; cook until caramel in color and very soft, 25-30 minutes. Add the sherry and stock.
Combine the beef with Worcestershire sauce, parsley, Dijon, salt and pepper; form four patties.
Heat a griddle or cast iron pan over medium-high heat. Drizzle with EVOO and cook the patties for 7-8 minutes, turning once. Clean the griddle and return to the stovetop over medium heat.
Butter the bread slices on one side and build patty melts with butter sides out, stacking the bread, cheese, onions, a patty, more onions, cheese and bread.
Grill the sandwiches until crispy and golden and the cheese has melted. Serve the patty melts with a simple watercress salad and cornichons alongside; pass extra mustard at the table.