• For a gas grill: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Leave primary burner on high and turn off other burner(s).
Clean and oil cooking grate. Place tenderloins on hotter side of grill. Cover and cook, turning tenderloins every 2 minutes, until well browned on all sides, about 8 minutes.
For the salsa: Brush pineapple and onion with 1 teaspoon oil. Move tenderloins to cooler side of grill (6 to 8 inches from heat) and place pineapple and onion on hotter side of grill. Cook until pineapple and onion are charred on both sides, 8 to 10 minutes, and until pork registers 140 degrees, 12 to 17 minutes, turning tenderloins every 5 minutes. As pineapple, onion, and tenderloins reach desired level of doneness, transfer pineapple and onion to plate and transfer tenderloins to carving board and let rest for 10 minutes.
While tenderloins rest, coarsely chop pineapple. Pulse pineapple, onion, cilantro, serrano, lime juice, reserved spice mixture, and remaining 1 tablespoon oil in food processor until mixture is coarsely chopped, 4 to 6 pulses. Transfer to bowl and season with salt and extra lime juice to taste. Slice tenderloins into ½-inch-thick slices. Serve with salsa.
Nutrition information per serving: 381 calories; 92 calories from fat; 10 g fat (2 g saturated; 0 g trans fats); 164 mg cholesterol; 633 mg sodium; 16 g carbohydrate; 1 g fiber; 12 g sugar; 54 g protein.