Place the tuna, mayonnaise, anchovy paste, capers, lemon juice and water in a food processor and pulse until smooth; season with salt and pepper. Store sauce in the fridge until the veal is ready.
Preheat the barbecue or indoor grill to medium-high heat. Brush veal with oil and season with salt and pepper. Grill 2-3 minutes per side, or until just cooked through. Place veal on plates, top with tuna sauce, sprinkle with chopped parsley, garnish with lemon and serve.