For the dressing-marinade mixture, in a small bowl whisk together lime juice, garlic, cumin, salt, and pepper. Reserve 1/4 cup of the mixture for the dressing in the refrigerator. For the marinade, transfer remaining mixture to a self-sealing plastic bag. Add chops; seal bag and refrigerate for 2 to 4 hours.
Prepare a medium-hot fire with charcoal or preheat gas to medium high. Lightly oil grill grate.
Remove chops from marinade (do not pat dry), discarding marinade from the bag. Grill chops and pineapple directly over heat, turning once, until internal temperature of pork on a thermometer reads between 145 degrees F. (medium rare) and 160 degrees F. (medium), followed by a 3-minute rest , about 8 to 11 minutes.
Plate greens on 4 dinner dishes. Divide pineapple,black beans, and onion onto plates. Top with pork chops. For the dressing, whisk the 3 tablespoons of oil and honey into the reserved dressing mixture; drizzle atop salads.
*Cuban cooking often calls for sour orange juice, which is less sweet and more acidic than common orange juice. If you can find sour oranges, such as Seville or Bergamont, substitute this juice for the lime juice. You can also use half lime juice and half orange juice.
For a super-quick side, warm flour tortillas on the grill or griddle pan just until heated through and cut into wedges. Serve tortilla wedges with whipped honey-butter.
4 New York (top loin) pork chops, 3/4-inch thick
2/3 cup lime juice, *
3 cloves garlic, minced
1 teaspoon ground cumin
1/2 to 1 teaspoon salt
1/4 teaspoon black pepper
4 1/2-inch thick slices fresh pineapple, cored
5 ounces arugula, watercress, or assorted baby greens
1 14 1/2-oz can black beans, drained and rinsed
1/2 small red onion, cut into thin slivers
3 tablespoons olive oil, (plus oil for the grill grate)
1 teaspoon honey