Combine the chiles, garlic, paprika, and 1 Tablespoon salt in a food processor and pulse to form a rough paste. Transfer the mixture to a large bowl and stir in the white and red wines until smooth. Add the pork pieces, turning to coat. Cover the bowl with plastic wrap and refrigerate overnight, or for up to 48 hours.
Position a rack in the middle of the oven and preheat to 375°F.
Coat the bottom of a roasting pan with the oil. Add the pork, with the marinade and season with salt and pepper.
Roast, uncovered, turning the pork often, until it is evenly browned and an instant-read thermometer inserted into the middle of a piece of pork registers just under 150°F (about 1 hour).
Remove the pan from the oven and let the pork rest for 5 minutes. Thinly slice the pieces of pork against the grain and serve immediately.