Melt 2 tablespoons butter in a medium skillet over medium heat. Add onions and season with salt, pepper and thyme; cook until caramel in color and very soft, 25-30 minutes. Add sherry and stock.
Combine beef with Worcestershire, parsley, Dijon, salt and pepper; form 4 patties. Heat a griddle or cast-iron pan over medium-high heat, drizzle with oil and cook patties 7-8 minutes, turning once. Clean griddle and return to stovetop over medium heat.
Butter bread slices on one side and build patty melts with butter sides out, stacking bread, cheese, onions, a patty, more onions, cheese and bread.