When all sides of the pork loin have been seared golden brown and the loin is firm to the touch, remove pan from heat. Transfer pork loin and thyme sprigs to a baking pan. Place baking pan in oven, and cook pork 10-12 minutes for medium (about 150° F internal temperature). For medium well, add about 3 minutes more cooking time; for well done, add about 5 minutes). While pork is cooking in oven, prepare vegetables: Pour off rendered pork fat from sauté pan, leaving just enough to coat the bottom of the pan (about 1 teaspoon). Place pan over medium-high heat and mushrooms. Cook without stirring or turning 3-4 minutes; add broccolini and cook, stirring frequently, 3-4 minutes more.