In a large bowl, whisk together the lime juice, orange juice, oil, oregano, salt and pepper. Add the onion and garlic and toss with your hands to combine. Add the beef and toss to coat. Cover the bowl tightly with plastic wrap and refrigerate for at least 1 hour and up to 12 hours.
Prepare a gas grill for two-zone heat: Set one burner at medium-high and one or two burners at high. (Alternatively, prepare a charcoal grill for high heat.)
Remove the steaks from the marinade, shaking off any excess and brushing off and reserving any onions that are stuck to the meat. Drain the onions in a fine-mesh sieve set over the sink — discard the marinade and save the onions.
Grill the beef over high heat, turning once, for 2 to 3 minutes per side for medium-rare. Transfer to a cutting board and let rest for 10 minutes.
If the onions have fallen apart, they will be easier to sauté rather than grill, unless you have a vegetable grill basket—and if you do, I recommend using it (even if the onions didn’t fall apart, a grill basket will help prevent them from slipping through the grill grates). Grill or sauté the onions until they are charred on all sides, for 4 to 8 minutes. Transfer to a plate.
Grill the chorizo, turning occasionally, until charred on all sides and cooked through, for 2 to 3 minutes per side.
Grill the whole jalapeños and scallions over medium-high heat, turning occasionally, until charred and tender, for 4 to 8 minutes. Transfer to a large bowl and toss with a squeeze of lime juice, a drizzle of oil and a pinch of salt.
To make the quesadillas, toast one side of the tortillas over the medium-high side of the grill until lightly charred, for about 1 minute. Flip and place a small mound of cheese on the charred side, then fold in half like a taco and continue to grill until the cheese begins to melt and the tortilla is lightly charred, for about 1 minute. Flip again to char the other side.
Serve the quesadillas along with grilled tortillas and you can make tacos or stuff the quesadillas with carne asada, chorizo, chiles jalapeños, scallions, guacamole, salsa tatemada and cilantro. Serve with the refried beans and lime wedges for squeezing.
Ask your butcher to slice the steaks lengthwise into 1/3-inch-thick steaks. These thin cuts take to the marinade quicker and also cook faster on the grill. If you’re grilling flanken short ribs, strip or rib eye, cut into 2-inch-wide pieces. If you’re grilling flank or skirt, slice against the grain into 1/2-inch-thick strips.