1. Cut 1/2-inch-deep slits all over pork; place meat in a large plastic food bag.
2. In a food processor or blender, combine cider, soy sauce, peanut butter, thyme, chili flakes, and garlic. Whirl until well blended.
3. Pour cider marinade over pork, seal bag, turn to coat meat with marinade, then set in a pan. Chill, turning occasionally, for at least 30 minutes or up to 1 day.
4. Lift meat from marinade and set on a rack in a 9- by 13-inch pan. Reserve marinade.
5. Bake pork in a 350° oven until a thermometer inserted in center of thickest part reaches 150° to 155°, 1 1/4 to 1 3/4 hours; after 40 minutes, baste with some of the reserved marinade. Transfer pork to platter and let stand 5 to 10 minutes in a warm place.
6. As pork rests, pour remaining marinade into pan with pork juices. (If pork drippings are burned, do not use. Instead pour marinade into a 10- to 12-in. frying pan.) Stir to scrape browned bits free. Then stir often over high heat until the sauce is reduced to about 1 cup, 6 to 8 minutes. Pour into a bowl.
7. Slice the pork and accompany the meat with sauce.