In a large resealable plastic bag, combine the paprika, ancho powder, garlic powder, onion powder, sugar, chipotle, cumin, coriander, salt, and pepper. Add the lime juice and oil and shake the bag to blend. Add the steak and seal the bag. Let the steak stand at room temperature for 2 hours.
Light a grill or preheat a grill pan. Grill the steak over moderately high heat, turning twice, until lightly charred on the outside and medium-rare within, about 10 minutes. Transfer the steak to a work surface and let rest for 10 minutes. Thinly slice the steak and serve with tortillas, pico de gallo, avocado salsa, and cabbage.