In a medium mixing bowl, combine fresh orange juice, fresh lime juice, minced garlic, minced jalapeño (if using), olive oil, chopped cilantro, ground cumin, chili powder, smoked paprika, dried oregano, kosher salt, black pepper, soy sauce, and white vinegar. Whisk thoroughly until the oil is incorporated.
Trim any excess silver skin or thick fat from the skirt or flank steak. Pat the steak completely dry on both sides with paper towels. If using a very long skirt steak, cut it into two or three manageable pieces.
Place the steak in a large zip-lock bag or glass container and pour the marinade over it, ensuring all surfaces are coated. Seal and refrigerate for a minimum of 2 hours and up to 12 hours. Remove from the refrigerator 30-45 minutes before grilling.
Preheat your outdoor grill or cast iron grill pan to high heat (450-500°F / 230-260°C). Lightly oil the grill grates with a neutral oil. Ensure the grill is screaming hot before adding the steak.
Remove the steak from the marinade, shaking off excess. Place it directly on the hottest part of the grill. Grill skirt steak for 3-4 minutes per side, or flank steak for 4-6 minutes per side, for medium-rare (130-135°F internal). Do not press down on the meat. Flip only once during cooking.
Insert an instant-read thermometer into the thickest part of the steak to check doneness. 125-130°F is rare, 130-135°F is medium-rare (recommended), and 135-145°F is medium. Continue grilling in 1-minute increments if needed.
Transfer the steak to a clean cutting board and tent loosely with aluminum foil. Let it rest for 5 to 10 minutes to allow the juices to redistribute.
Identify the direction of the grain and slice the steak thinly, at a 45-degree angle, directly against the grain into about 1/4 inch (6mm) thick slices. Arrange on a serving platter and squeeze fresh lime over the top before serving.