For the dough: Combine the flour, salt, and sugar in the bowl of a food processor and pulse until combined. Scatter the lard and butter over the top and pulse a few times until it resembles coarse meal.

Whisk together the egg yolk, water, and vinegar in a measuring cup. Add the mixture to the dough, pulsing until just combined. Turn the dough out onto a work surface and gently knead until it just comes together. Form the dough into a disk, cover with plastic wrap, and refrigerate for at least 1 hour and up to 6 hours. Roll out thinly. Cut into 4-inch circles.

For the short ribs: Preheat the oven to 350 degrees F.

Heat the oil over high heat in a Dutch oven until it begins to shimmer. Season the short ribs on both sides with salt and pepper and cook until golden brown on both sides. Remove to a plate.

Drain all but 2 tablespoons of the fat from the pan, add the garlic, and cook until it is lightly golden brown. Add the wine and cook until almost completely reduced. Add the currant juice, chicken stock (enough to cover the ribs by three-quarters), and chiles and bring to a boil. Add the ribs, cover, and transfer to the oven. Cook until fork tender, about 2 hours. Remove the short ribs to a platter or bowl and tent with foil.

Transfer the cooking liquid to a food processor and process until smooth. Strain into a large saute pan and cook until reduced by half. Remove the meat from the bone, shred, and add to the reduced cooking liquid. Season with salt and pepper. Let cool slightly.

Add enough canola oil to fill a Dutch oven three-quarters of the way. Heat to 375 degrees F on a deep-frying thermometer.

Fill each dough round with some meat, top with some goat cheese and pickled onions. Seal the edges with a little water and crimp with a fork. Fry, turning halfway through, until evenly golden brown, 3 to 5 minutes. Serve with Piquillo Pepper Sauce.

Bring the vinegar, lime juice, water, sugar, and salt to a boil in a small saucepan. Remove from the heat and let cool for 10 minutes. Put the onions in a medium bowl, pour the vinegar over, cover, and refrigerate for at least 4 hours and up to 48 hours before serving.

Heat the oil in a medium saute pan over medium high heat. Add the onions and cook until soft, about 4 minutes. Add the garlic and cook for 30 seconds. Stir in the piquillo peppers, season with salt and pepper, and cook 5 minutes.

Transfer the mixture to a blender, add the vinegar, and blend until smooth. Add the cilantro and creme fraiche and pulse a few times just to incorporate. Transfer to a bowl. Serve at room temperature.