Instructions

Cut 1 small head (1¼ pounds) red cabbage through core into 1-inch-wide wedges. Rub all over with 1 tablespoon extra-virgin olive oil and sprinkle with ¼ teaspoon table salt and ¼ teaspoon pepper. Pat 4 salmon fillets dry with paper towels, rub all over with 2 teaspoons  extra-virgin olive oil, and sprinkle flesh side with ½ teaspoon salt and ½ teaspoon pepper. Grate 2 teaspoons zest from 2 limes, then halve limes.
Grill cabbage and lime halves over hot fire (covered if using gas) until lightly charred and cabbage is beginning to wilt, 4 to 8 minutes, flipping cabbage halfway through. Transfer to cutting board to cool while grilling salmon.
Add salmon to now-empty grill, flesh side down and perpendicular to grate bars. Grill salmon fillets, covered (reducing heat to medium if using gas), and cook until well marked and salmon registers 125 degrees (for medium-rare), 4 to 6 minutes per side; transfer to serving platter.
Once lime halves and cabbage are cool enough to handle, juice limes to yield ¼ cup and thinly slice cabbage, discarding core. Whisk lime zest and juice, 1 tablespoon toasted sesame oil, and remaining 2 tablespoons extra-virgin olive oil, ¼ teaspoon salt, and ¼ teaspoon pepper together in large bowl. Add sliced cabbage and 1 Asian pear, unpeeled, cored, and shredded, and toss to coat, then season with salt and pepper to taste. Serve with grilled salmon.