Ingredients

• 1 red onion, halved, thinly sliced
• 1 1/2 cups boiling water
• 1 cup plus 2 tablespoons orange juice
• 6 tablespoons distilled white vinegar
• 1/2 teaspoon (scant) salt
• 1 garlic clove, peeled
• 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
• 1/2 cup olive oil
• 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
• *Available at some supermarkets and specialty foods stores, and from tienda.com.

Instructions

1. 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.
2. For vinaigrette: 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.
3. 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.
4. For pork: 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.
5. 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.
6. 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.
7. 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.