- Combine ¼ cup balsamic vinegar; 1 tablespoon honey; 1 tablespoon Dijon mustard; 2 garlic cloves, minced to paste; 1 teaspoon chopped thyme leaves; 1 teaspoon kosher salt, and ½ teaspoon pepper in large bowl. Gradually whisk in ¼ cup extra-virgin olive oil until smooth. Pat 10 chicken thighs dry and add to marinade, turning to coat. Cover and marinate for at least 1 hour or up to 6 hours.
- Meanwhile, combine ¼ teaspoon red pepper flakes, remaining ½ cup balsamic vinegar, remaining 2 tablespoons honey, and ¼ teaspoon salt in small saucepan. Bring to boil over medium-high heat, then reduce heat to medium-low and simmer until reduced by half, 10 to 15 minutes; set aside to cool.
- When ready to grill, place 1 pound peaches, halved, and ½ small red onion, halved, on large plate and drizzle with remaining 1 tablespoon oil and sprinkle with remaining ¼ teaspoon salt.
- FOR A CHARCOAL GRILL: Open bottom vent completely. Light large chimney starter two-thirds filled with charcoal briquettes (4 quarts). When top coals are partially covered with ash, pour evenly over grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Reduce all burners to medium-high.
- Clean and oil cooking grate. Brush cut side of peaches and onion with 1 tablespoon glaze. Arrange fruit and onion cut side down on grill and grill until well charred, turning once halfway through, about 4 minutes. Transfer to large plate and let cool slightly.
- Grill chicken for 6 to 8 minutes on each side, covered, until nicely browned on both sides and meat registers at least 175 degrees. Transfer chicken to serving platter and brush with 1 tablespoon glaze.
- Cut peaches in half crosswise to create quarters and thinly slice onion; transfer peaches and onion to large bowl. Add 1 tablespoon glaze and toss to coat.
- Spoon peaches and onions over chicken. Sprinkle with 1⁄2 cup basil leaves, torn, and drizzle with extra oil. Serve, passing any remaining glaze.
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