Have butcher cut the chine bone in between each rib of the pork roast to make carving easier. Leave the fat cap on for added moisture and flavor. Line a large stockpot or bucket with a plastic bag. Pour water into the bag and dissolve salt and brown sugar. Add peppercorns and a few thyme sprigs. Place the pork roast in the bag of brine. Tie the bag closed so the pork is submerged. Refrigerate for 6 hours, the brine will tenderize the meat. Remove pork from the brine and dry thoroughly with paper towels.
Preheat oven to 400 degrees F. Lay thyme sprigs all over the pork roast, season with salt and pepper, then secure with butcher's twine to help hold the shape. Coat a roasting pan with a little olive oil and set on 2 burners over high heat until almost smoking. Sear the pork, fat side down, until caramelized. Turn the roast to brown all sides, this should take about 10 minutes. To flavor the pork drippings, scatter carrots, garlic, onion, shallots and more thyme sprigs in the pan, then transfer the roast to oven. Roast until a meat thermometer inserted in the thickest part of the roast registers 150 degrees F, approximately 1 hour.
Heat olive oil in a large deep skillet over medium heat. Brown the sausage links on all sides until cooked through. Remove the links from the pan and slice on a bias. Add slivered garlic, red pepper flakes and fennel seed, stir to incorporate. Return the sausage back to the pan, along with broccoli rabe and chicken broth. Saute with the stock for 5 minutes until the rabe is wilted.
Whisk together balsamic vinegar, honey, mustard seed, tarragon, and about 1/4 cup olive oil. Slice peaches in half lengthwise and remove pits. Pour the marinade over the peaches, tossing to coat. Place peaches cut side down in a baking pan and roast for 12 to 15 minutes until soft.
Remove the pork to a cutting board and let it rest while preparing the pan sauce. Discard the aromatic vegetables from the roasting pan, set pan on 2 burners over medium heat. Deglaze with apple juice, scraping up the brown bits stuck to the bottom of the pan. Reduce by a third. Season with salt and pepper; whisk in butter to smooth out.
Cut the twine and carve the roast. Serve family style on a platter with broccoli rabe, sausage, and roasted peaches. Drizzle sauce over meat before serving.
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