Special equipment: 2 cups pecan wood chips, soaked in water for 2 hours; soaked rosemary sprigs or sage leaves, optional
Tie the loin with kitchen twine at 1-inch intervals and add to the Honey-Rosemary Brine in a large container. Brine the pork loin in the refrigerator for at least 4 hours and up to 12 hours. Remove from the brine, rinse under cold water and pat dry with paper towels. Let sit at room temperature for 1 hour before grilling.
Prepare the charcoal in a chimney starter (allowing the charcoal to burn until all the charcoal is covered with a thin layer of gray ash) and add to the grill, creating a two-level fire by spreading the coals out over half the grill bottom, piling them up in a mound 3 briquettes high, leaving the other half with no coals. Spread the soaked wood chips evenly over the top and the rosemary sprigs or sage leaves, if desired. Put the cooking grate in place and open the grill lid vents halfway. Let the grate heat for 5 minutes. Use a grill brush to scrape the cooking grate clean.
Brush the entire loin with the olive oil and sprinkle with pepper. Place the pork on the opposite side of the coals but close to the fire. Cover with the lid and turn the lid so that the vents are opposite the fire to draw smoke through the grill. Use a grill thermometer and make sure the heat inside the grill is at 400 degrees F.
Grill the pork, covered, until an instant-read thermometer inserted into the thickest part of the pork registers about 135 degrees F. This will take anywhere from 30 to 45 minutes, depending the thickness of the loin.
Transfer the loin to a cutting board, tent loosely with foil and let rest 15 minutes before cutting into thick slices. Serve with the Agrodolce Grilled Peaches and drizzle some of the reduced peach glaze over the meat.
Bring 6 cups water to a boil in a large saucepan. Add the broth, salt, honey, sugar, peppercorns, rosemary and garlic, stirring to dissolve the salt. Remove from the heat and add the ice cubes to cool quickly to room temperature.
Bring the vinegar, honey, nectar and some salt and pepper to a simmer in a large high-sided saute pan over medium heat. Cook until the liquid is reduced to a syrupy consistency, about 15 to 20 minutes. Remove from the heat.
Brush the cut side of the peaches with the canola oil, season with salt and pepper and place cut-side down on the grill over medium-high heat. Grill until lightly golden brown, 2 to 3 minutes. Flip, cook 1 to 2 minutes then brush with the glaze and cook another minute or so. The peaches should be tender but hold their shape. Transfer the peaches to a platter and drizzle with some of the glaze.