Heat 1 tablespoon of the oil in a small saucepan over high heat. Add the ginger and garlic and cook until softened, about 2 minutes. Whisk in the hoisin sauce, ketchup, sherry, soy sauce and sesame oil and bring to a boil. Remove from the heat and cool slightly.
Mix together the beef with the cilantro, 1 teaspoon salt and 1/4 teaspoon black pepper using your hands until just combined. Form into four 3/4-inch-thick patties, about 4 1/2 inches in diameter. Heat a grill to medium-high heat. Cook the burgers, turning once, about 4 1/2 minutes per side for medium, brushing the burgers with some of the sauce in the last few minutes of cooking time.
Serve the burgers on the buns with the extra sauce on the side, lettuce and tomato on top if using, and pickles and fries on the side.