Melt butter in a large skillet over medium-high heat until lightly browned. Add mushrooms, and sauté 4 to 7 minutes or until lightly browned and tender. Stir in plum sauce, soy sauce, and ginger. Bring to a boil, reduce heat, and simmer, stirring often, 3 to 4 minutes. Keep warm.
Heat oil in a large nonstick skillet over medium-high heat. Sprinkle tuna evenly with pepper, and cook 4 minutes on each side (rare) or until desired degree of doneness. Serve with warm sauce.
*Freshly ground black pepper may be substituted.
Note: For testing purposes only, we used Honan Plum Sauce. Look for plum sauce in the ethnic foods aisle of the supermarket.