Heat 6 Tbsp. oil over high heat in a large saucepan. Sweat onions in oil and add the beef when you start smelling the aroma of the onions, about 5 minutes.
Cook over medium heat until juice from the beef evaporates, 10-12 minutes, and then add tomato paste.
Season with salt to taste. Add all other ingredients except the tomato, parsley, and eggs.
Lower heat to bring to a simmer and let the meat stew in its juices, 10-12 minutes. Taste for seasoning and add eggs, tomato, and parsley.
Stuff pastry dough with the filling by carefully placing the filling in the middle of the pastry and then close the edges of the pastry by bringing them together. Use a fork to press the new edge closed.
Make a simple egg wash by beating together 1 egg and 1 tsp. water in a small bowl. Brush the empanadas with the wash before baking.
Bake at 375 °F, about 9-12 minutes, depending on the oven, until golden brown.