Make the filling: Melt butter in a large skillet over medium heat. Add onion, garlic, oregano, cumin, salt, and pepper; cook and stir until onion is golden brown, 5 to 7 minutes. Add pork and cook until completely browned and crumbly, 7 to 10 minutes more. Drain fat from the skillet. Stir in raisins, olives, and hard-cooked eggs.

Whisk water and cornstarch together in a small bowl; pour into the skillet and stir until liquid thickens. Remove from the heat and set aside.

Make the dough: Whisk milk and melted shortening together in a bowl until evenly blended. Stir flour and salt together in a separate large bowl. Pour milk mixture into the flour mixture; whisk until well combined and a dough forms. Let rest for 10 minutes.

Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.

Roll dough on a lightly floured surface to a thickness of 1/8 inch. Cut into 12 circles with a round cookie cutter or glass. Spoon filling into the center of each circle. Fold each circle in half and press the edges with a fork to seal. Brush the tops with beaten egg. Place empanadas onto the prepared baking sheet.