1. To prepare pork, add pork chops to Basic Brine; refrigerate for 16 hours, turning occasionally.
2. To prepare glaze, combine 2/3 cup sugar, 1/3 cup water, jalapeño pepper, and garlic in a small saucepan; bring to a simmer, stirring just until sugar dissolves. Stir in green onions and lime juice. Remove from heat, and let stand for 1 hour.
3. Prepare charcoal grill to high heat. Set up an elevated grill rack 18 inches above surface of coals, using a second grill rack that is set atop 2 stacks of 2 bricks each.
4. Tie herb sprig bunches tightly to the handle of a long wooden spoon.
5. Remove pork from brine. Pat pork dry with paper towels; discard brine. Place pork on elevated grill rack; grill 1 minute on each side. Grill 8 minutes, turning every 2 minutes. Grill 1 minute on each edge of pork. Continue grilling until a thermometer registers 115°, turning and basting with herb brush and jalapeño glaze every 2 minutes (about 26 minutes total). Remove pork to a platter; lightly baste. Let stand 15 minutes. Maintain grill at medium-high heat.
6. Carefully remove the elevated grill rack and bricks. Place pork on the lower grill rack; grill 7 minutes or until thermometer registers 140°, turning and basting every 1 minute. Singe herbs for 5 seconds after final basting. Finely chop herbs; reserve.
7. Combine olive oil, parsley, black pepper, salt, and reserved chopped herbs on a cutting board. Add pork to oil mixture; turn to coat. Let stand 10 minutes. Cut pork into thin slices. Turn slices on board dressing to coat. Serve pork with dressing.
Basic Brine: Combine 5 cups water, 1/4 cup kosher salt, 1 tablespoon black peppercorns, 1 tablespoon chopped fresh thyme, 1 tablespoon sugar, 8 garlic cloves, 3 bay leaves, and 1 halved lemon in a medium saucepan; bring to a boil. Remove from heat; cool. Refrigerate brine overnight.
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