Preheat oven to 250 degrees. Place a double layer of foil large enough to wrap ribs on a rimmed baking sheet (to catch any drips). Set ribs on top and generaously season with salt and pepper.
Pulse chilies, garlic, oil, vinegar, rosemary, and red pepper flakes in a food processor until mixture is almost smooth (a few larger pieces should still be visible). Rub ribs all over with marinade and pour any excess over top. Wrap up tightly in foil.
Roast ribs until meat is tender but not quite falling off the bone, 2 1/2- 3 hours. To check doneness, run a paring knife through 2 or 3 ribs; it should slide easily into flesh.
Heat broiler. Once ribs are cool enough to handle, remove foil and reserved juices. Place ribs on a clean rimmed baking sheet and broil until charred in spots and marinade has formed a golden-brown crust, 8-10 minutes. Transfer to a cutting board and let rest at least 10 minutes.
Slice meat into individual ribs. Drizzle with reserved juices and top with parsley. Serve with lemon wedges.