For the pickled onions, in a small bowl, toss the onion and lime juice. Season with salt and pepper; let stand.
Preheat a grill or griddle pan over medium-high.
For the dressing, in a large bowl, whisk the shallot, 3 tbsp. oil, vinegar, Tabasco, garlic, honey and cumin; season.
Season the steaks; drizzle with oil. Grill, turning occasionally, until the steaks are crispy and browned on the outside but still tender in the center, 8 minutes for hanger steak or flatiron, 5 to 6 minutes for skirt steaks. Let rest 10 minutes, then slice against the grain.
Toss the pickled onions, greens, jalapeno rings, chips and cheese with the dressing. Divide the salad among plates; top with the sliced steak.