- 1 red onion, halved, thinly sliced
- 1 cup plus 2 tablespoons orange juice
- 6 tablespoons distilled white vinegar
- 1/2 teaspoon (scant) salt
- 1/2 teaspoon smoked salt or coarse kosher salt
- 3 tablespoons purchased tomato-based barbecue sauce
- 2 tablespoons orange juice
- 2 tablespoons fresh lime juice
- 1 tablespoon coarsely ground black pepper
- 1 tablespoon smoked Spanish paprika (Pimentón de La Vera)*
- 1 teaspoon smoked salt or coarse kosher salt
- 2 (1-pound) pork tenderloins
- Nonstick vegetable oil spray
- 6 large onion rolls, split, toasted
Place sliced onion in medium bowl. Pour boiling water over. Let stand 10 minutes; drain well, then return to bowl. Add juice, vinegar, and salt and stir to blend. Cover and chill at least 2 hours and up to 1 day.
Chop garlic with salt to paste; scrape into small bowl. Add barbecue sauce, orange juice, and lime juice to bowl. Gradually whisk in oil. Season vinaigrette to taste with pepper. DO AHEAD Can be made 1 day ahead. Cover and refrigerate.
Blend pepper, smoked paprika, and salt in small bowl. Sprinkle seasoning mix evenly over both tenderloins. Let stand at least 30 minutes and up to 2 hours.
Spray grill rack with nonstick spray. Prepare barbecue (high heat). Grill tenderloins uncovered 5 minutes, rolling over to sear all sides. Cover grill and continue to cook until thermometer inserted into thickest part registers 145°F, turning often and moving to cooler part of grill as needed, about 15 minutes longer. Transfer to cutting board; let rest 10 minutes.
Thinly slice tenderloins crosswise into rounds. Mound pork on roll bottoms. Top with well-drained onion slices, then drizzle with vinaigrette. Cover with roll tops and serve, passing extra onion slices and vinaigrette separately.