Make the dough: In a large bowl, whisk together the olive oil, water, and salt. Gradually add in the flour, one cup at a time, stirring with a wooden spoon. Add each addition after the previous is almost fully incorporated. Once all the flour is added, the mixture will seem clumpy. Scrape the dough onto a clean work surface and knead by hand until the dough comes together and no dry bits of flour remain, 1 to 2 minutes. The dough should be relatively smooth, malleable, and no longer stick to your hands or the counter. Transfer the dough back into the bowl, cover, and let rest while preparing the filling.
Make the filling: In a large frying pan set over medium heat, add the olive oil. Once it is shimmering, but not smoking add the diced onion, diced red pepper, and bay leaf. Cook for 6 to 7 minutes, stirring occasionally with a wooden spoon, until softened and the vegetables begin to caramelize.
Add the beef: Add the ground beef, salt, black pepper, and sweet paprika. Cook for 4 minutes, stirring to break up the beef, until browned.
Add the tomatoes and reduce: Add the tomatoes and scrape the bottom of the pan with the wooden spoon to loosen the flavorful browned bits. Reduce the heat to low and cook for 8 to 10 minutes until almost all the liquid has evaporated.
Finish the filling: Add the garlic and parsley and cook for 1 minute until fragrant. Take the pan off the heat and stir in the chopped, hard-boiled egg and olives. Set aside until cool enough to handle.
Preheat the oven: Arrange oven racks in the upper and lower thirds of the oven and preheat to 400°F. Line two baking sheets with parchment paper.
Assemble the empanadillas: Divide the dough into 16 equal pieces. Shape each piece into a sphere. Work with one piece of dough at a time and keep the others covered to prevent them from drying out. Use your palms to press each ball of dough into a circle about 5 inches in diameter, or use a rolling pin. Add about 2 tablespoons of filling to the center of the dough. Fold the dough over the filling and gently seal the edges with your fingers. Use your fingers to form the crimp by twisting and folding the edges together. Alternatively, use the tines of a fork to press and seal the edges together.
Bake: Arrange the assembled empanadillas on the lined baking sheets, placing 8 on each sheet. In a small bowl, whisk the egg with a tablespoon of water. Use a pastry brush to brush the top of each empanadilla with the egg wash. Bake for 20 minutes, or until golden brown, rotating the pans and switching shelves halfway through.
Store leftover empanadillas in an airtight container in the refrigerator for up to 4 days. Reheat them at 350°F for about 15 minutes, or until warmed through. This retains the texture of the crust.
Beef empanadillas can also be frozen for up to 3 months either before baking, or after. In either case, freeze in a single layer on a sheet pan. Once frozen, transfer to a freezer bag or freezer-safe container. For uncooked frozen empanadillas, bake from frozen at 400°F until cooked through, about 25-30 minutes. Rotate the pans and switch shelves halfway through baking. To reheat cooked frozen empanadillas, bake in a 350°F oven for 15 minutes.