Boil water and add garlic cloves, cooking until very tender, 15 to 20 minutes. Rinse garlic under cold water for 30 seconds and set aside. Preheat oven to 450°F.
In a mixing bowl, combine 6 cooked garlic cloves with olive oil. Mash together with a fork or whisk, adding thyme and salt and pepper to taste. Rub lamb with herb garlic mixture, coating completely and arrange loins on a baking sheet.
Heat 2 TBSP olive oil in a large ovenproof sauté pan over high heat. Add the lamb loins and cook just until browned on each side, about three minutes. Place the sauté pan in the preheated oven and cook the meat until medium rare, about 8 minutes. Remove from oven; place lamb on cutting board and allow to rest.
Warm the remaining TBSP olive oil in the sauté pan over high heat. Add the 10 remaining garlic cloves and sauté until lightly browned, 2 to 3 minutes. Add the wine and deglaze by stirring and scraping all sides of the sauté pan. Cook until the wine reduces by half. Add the stock and bring to a boil. Reduce heat and swirl in the butter and season with salt and pepper to taste.
Cut the lamb loins into 3/4-inch-thick slices. Spoon the sauce evenly over the lamb. Scatter garlic around each plate.