In a small bowl, whisk together the soy sauce, Worcestershire sauce, sugar, mustard, and oil until combined.
Pour marinde over tuna and gently turn steaks until well-coated on each side. Cover with plastic wrap and refrigerate for at least 30 minutes up to 2 hours.
Prepare grill. Remove tuna and reserve marinade for basting. Grill tuna for about 10-15 minutes, turning once and basting often with reserved marinade.
Serve tuna steaks with lemon wedges and garnished with chopped parsley.
