For the chimichurri sauce: Combine the parsley, oregano, cilantro, garlic, crushed red pepper and 1 1/2 teaspoons salt in a food processor. Process until coarsely chopped. Add the vinegar and pulse to combine. Scrape the mixture into a bowl and whisk in the oil and 2 tablespoons water. Set aside at room temperature. (Can be made 1 day ahead and refrigerated; bring to room temperature before serving. Makes 1 cup.)
For the filling: Put a rack in the upper third of the oven and preheat to 425 degrees F. Put the chicken thighs skin-side down in a large saucepan. Add the broth, parsley sprigs and bay leaf, turn the heat to medium-high and bring to a simmer. Cover, reduce the heat to low, and simmer until a meat thermometer inserted in a piece of chicken near the bone registers 150 degrees F, about 15 minutes. Transfer the chicken to a plate. When cool enough to handle, discard the skin and shred the meat into large pieces; you should have about 2 cups. Place in a medium bowl. Reserve 1/2 cup of the broth. (Strain and keep the rest to make delicious soup!).
Wipe out the saucepan, heat it over medium heat and add the lard. Add the onion, season with salt and cook, stirring, until soft but not brown, about 4 minutes. Sprinkle with the cumin and crushed red pepper and cook, stirring, 30 seconds. Stir in the flour. Whisk in the 1/2 cup broth and let it bubble and thicken, stirring frequently, about 4 minutes. Pour the mixture over the chicken, add the olives and toss to combine. Taste and add salt if necessary-the filling should be aggressively seasoned, since it will be wrapped in the dough. Pop the chicken into the refrigerator just until cool, about 10 minutes.
To make the empanadas: Place a small bowl of cool water by your work surface. Line a sheet pan with parchment paper. Working with 1 wrapper at a time and keeping the rest covered, brush a little water on one edge of the empanada wrapper. Put 2 tablespoons of filling in the center of the wrapper and fold in half. Use your finger to press out the air, making a border of about 1/2 inch around the filling. Press with a fork to seal the edges. Transfer to the prepared sheet pan. Repeat with the remaining wrappers and filling.
Bake the empanadas until golden brown, about 15 minutes, rotating the baking sheet halfway through. Serve warm with the chimichurri sauce.
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