In a large mixing bowl, combine 2 1/2 cups of all-purpose flour and 1/2 teaspoon of salt. Gradually mix in 1/2 cup of olive oil and 1/2 cup of cold water until a dough forms. Knead lightly until smooth, then cover with a cloth and let it rest for about 30 minutes.
In a skillet, heat 1 tablespoon of olive oil over medium heat. Add the diced onion and red bell pepper, sautéing until softened. Stir in the ground beef, cooking until browned. Add 3/4 teaspoon of salt, 1/2 teaspoon of ground black pepper, and 1 teaspoon of sweet paprika. Mix in the diced tomatoes, minced garlic, chopped green olives, and parsley. Cook for an additional 5-7 minutes until well combined. Remove from heat and let cool slightly.
On a floured surface, roll out the rested dough to about 1/8-inch thickness. Use a cookie cutter or glass to cut out circles, approximately 4-5 inches in diameter.
Place a generous tablespoon of filling in the center of each dough circle. Fold the dough over to create a half-moon shape and press the edges together to seal. You can crimp the edges with a fork for a decorative touch.
Preheat your oven to 375°F (190°C). Place the empanadillas on a baking sheet lined with parchment paper. Brush the tops with the beaten egg to give them a beautiful golden finish.
Bake in the preheated oven for 20-25 minutes, or until golden brown. Keep an eye on them, as baking times may vary.
Remove the empanadillas from the oven and let them cool slightly before serving. Enjoy them warm with your favorite dipping sauces or on their own!