In a small bowl, combine the thyme, rosemary, garlic, the 1 1/2 Tbs. salt, pepper and olive oil. Rub the herb mixture on all sides of the pork loin. Cover with plastic wrap and refrigerate overnight.
Put the figs in a bowl, add the vermouth and soak for 1 hour. Strain the figs, reserving the soaking liquid.
Preheat an oven to 475°F.
Put the pork in a roasting pan and roast for 20 minutes. Reduce the heat to 400°F and continue roasting until an instant-read thermometer inserted into the thickest part of the meat, away from the bone, registers 140°F, 45 to 50 minutes more. Transfer the pork to a carving board, cover loosely with aluminum foil and let rest for 20 minutes.
Set the roasting pan over medium-high heat. Add the reserved soaking liquid and bring to a boil, stirring to scrape up the browned bits from the pan bottom. Reduce the heat to medium and add the figs, stock, demi-glace and fig balsamic vinegar. Simmer for about 5 minutes. Whisk in the butter 1 Tbs. at a time, and season with salt and pepper.
Carve the pork roast between the bones and arrange on a warmed platter. Pour the sauce over the meat and serve immediately. Serves 6 to 8.