In a large, shallow dish, whisk the garlic, anchovy paste, tomato paste, mirin, Worcestershire sauce, soy sauce and EVOO. Season the marinade with pepper, then add the meat, turning to coat. Let stand for 10 minutes while the grill pan or griddle heats over medium-high.
If using chicken, grill, turning occasionally, until cooked through, 12 to 15 minutes, then slice into 1/2-inch-thick pieces. If using steak, grill, turning occasionally, to desired doneness, 12 to 15 minutes. Let the steak rest, then slice into 1/2-inch-thick pieces.