Cut the pastry dough into strips of about 6 x 20 cm (approximately 2 x 8 inches).
Cook the potatoes in salted water for about 30 minutes, then peel and press through a ricer. Allow to cool slightly. Mix with the drained tuna, chopped shallot and garlic until smooth. Season with salt and pepper and add extra olive oil if necessary.
Brush the dough with butter and put a tablespoon of the tuna mixture at the beginning of each of the strips of dough. Fold up the strips (like a flag) into triangles. Place seam side down on a baking sheet lined with parchment paper and bake in a preheated oven at 160°C (approximately 325°F) for approximately 10 minutes or until golden brown. Serve warm.