Roughly chop the chorizo and process it into a paste using a stick blender. In a large non-stick skillet over high heat, warm the olive oil and sauté the onion and garlic for two minutes. Add the chorizo and cook for another two minutes. Stir in the ground beef and continue cooking until no pink remains. Incorporate the tomato paste and cook for one minute before adding the broth, passata, potato, thyme, oregano, cumin, paprika, cayenne, and salt. Simmer gently for 15 minutes until the potatoes are cooked and the mixture is juicy but not overly liquid. Stir in green onions, then transfer to a bowl and cool completely (approximately two hours).

Whisk the warm milk and egg yolk in a jug. In a food processor, pulse the flour, salt, and butter until the mixture resembles coarse crumbs, with no pieces larger than a pea. Add the milk-egg mixture and process briefly until a dough forms. Transfer to a floured surface and shape into a 20 cm log. Divide in half, form each into a 2 cm thick disc, wrap in cling film, and chill for 30 minutes or overnight. On a floured surface, roll out one disc to 3 mm thickness and cut out 15 cm circles, storing them layered with paper and covered in the refrigerator.

Preheat the oven to 220°C (425°F) or 200°C fan-forced. Spoon about 3 tablespoons (55g) of cold, pliable filling onto the upper half of a pastry circle. Flatten slightly into a half-moon shape, maintaining a 1.5 cm border. Add chopped olives and egg pieces. Brush the border with egg white, fold over, press to seal, and remove any trapped air. Crimp edges as desired or leave plain. Arrange on two baking trays, brush with egg yolk, and bake for 20 minutes or until golden and crisp.

Serve hot with your choice of dipping sauce.