Make the dough. Combine flour and salt in a large bowl. Cut in the cold butter using a pastry cutter or your fingers until the mixture looks like coarse crumbs. Whisk together the egg, cold water, and vinegar, then pour into the flour mixture. Stir until a dough forms, knead briefly, wrap in plastic wrap, and refrigerate for 30 minutes.
Cook the filling. Heat a skillet over medium-high heat. Add the ground beef and cook, breaking it apart, until browned. Drain excess fat. Add onion, bell pepper, and garlic, cooking for another 3–4 minutes until softened. Stir in cumin, smoked paprika, chili powder, tomato paste, and beef broth. Simmer for 5 minutes until the mixture thickens slightly. Season with salt and pepper. Stir in chopped hard-boiled eggs and olives if using. Let cool completely.
Assemble the empanadas. Preheat your oven to 400°F. On a lightly floured surface, roll the dough out to about 1/8-inch thickness. Cut into 5-inch circles using a bowl or round cutter. Place 2 tablespoons of filling in the center of each circle, fold over, and crimp the edges firmly with a fork to seal.
Bake. Arrange empanadas on a parchment-lined baking sheet. Brush the tops with egg wash. Bake for 22–25 minutes until golden and flaky.
Cool slightly and serve. Let them rest for 5 minutes before serving — if you can wait that long!