Heat oil in a large (12-inch) skillet over medium heat. Season pork chops on both sides with salt and pepper. Working in batches, if necessary, sear until brown on both sides, about 3 minutes per side. Transfer pork to a large plate or baking sheet.
Pour off fat from skillet, and return to low heat. Return pork and any accumulated juices to skillet; add milk and thyme sprigs. Bring to a boil over high heat; cover, and reduce heat to low. Simmer until pork is cooked through and tender, turning once, about 45 minutes.
Transfer pork to a serving platter, and cover with aluminum foil to keep warm. Return skillet to medium-high heat, and bring remaining liquid to a boil. Whisk together cornstarch and the water in a small bowl; whisk into liquid in skillet, and boil 1 minute. Transfer mixture to a blender or food processor. Add thyme leaves, and puree until smooth. Pour sauce over pork, and serve immediately.