Dough:
Line 2 large sheet pans with parchment paper. Set aside until ready to use.
Mix the flour and salt in the bowl of a food processor. Add the butter and pulse. Add the egg and the water or milk (in small increments) and continue pulsing until a clumpy dough forms. Split the dough into 2 large balls, and, flatten slightly. The dough can be used immediately or wrapped in plastic and refrigerated until ready to use (1-2 days).
When ready to use, lightly sprinkle flour on a clean surface, and roll out the dough into a thin sheet. Cut out round disc shapes (use a large circle cutter). Place discs on prepared sheet pans. Cover and chill for 20-30 minutes before filling.
Empanadas:
Preheat the oven to 375º F.
Add lamb, chorizo, garlic, onion, and peppers to a skillet over medium heat. Cook for 4-5 minutes. Add the tomato paste, paprika, and cumin; continue to cook for 6-8 minutes. Add the olives and cilantro, stir and remove from the pan from heat. Cool meat mixture before filling empanadas. Preferably chill (if you have time) in the refrigerator for 30 minutes or overnight.
Place 1 tablespoon of filling in the center of each disc, wet the edges, pinch both sides up and fold in half to seal. Use a fork to crimp the edges. Chill again at least 30 minutes the empanadas before cooking- this helps to prevent the filling from leaking out.
Bake or fry empanadas. Sprinkle a little coarse salt (optional) and serve with aioli. Enjoy!
To Bake: Place empanadas on parchment-lined sheet pans. Brush the center of the empanadas (not the edges) with the egg wash and bake for 18-20 minutes. Remove sheet pan from the oven and cool for 5 mins before serving.
To Fry: Add enough oil in a deep skillet to cover at least half of the empanadas. Heat oil on medium-high heat. When oil is hot (you can do a quick test by carefully dipping the tip of the empanada to the hot oil, if it sizzles then it’s ready) add empanadas a few at a time to the pan. Fry 1-2 minutes per side until golden brown. Place the fried empanadas on paper towels to drain any extra oil. Serve warm.
Aioli:
Place egg, garlic, and lemon juice in the bottom of a tall narrow glass, jar, or storage container. Pour oil on top and allow to settle for 15 seconds. Place the head of the immersion blender at bottom of the cup and switch it on. As aioli forms, slowly tilt and lift the head of the immersion blender until all oil is emulsified.
Transfer aioli to a medium bowl. Add sumac, mint leaves, and lemon zest; stir to combine. Whisking constantly, slowly drizzle in olive oil. Season to taste with salt and pepper.
