Combine beef with black pepper, ginger, garlic, scallions, Worcestershire and 2 tablespoons Tamari. Mix well and form 4 patties that are thinner at the center for even cooking.
Heat a cast-iron skillet with a tablespoon of peanut oil, a turn of the pan. Add burgers and cook 8 minutes, turning occasionally.
Heat a large skillet over medium-high heat with remaining 3 tablespoons oil over high heat. Add peppers and onions, and stir-fry 3-4 minutes to tender crisp. Add remaining tablespoon Tamari and wine or sherry, and reduce a minute. Melt in bean sauce and remove from heat; add in sesame oil.
Place burgers on buns, top with sherry-peppers and serve.