Place carrots and turnips in the bottom and up the sides of a 4-quart or larger slow cooker. Top with pork and scallion whites. Bring broth, water, soy sauce, sherry, brown sugar, ginger, vinegar, chile-garlic sauce to taste and garlic to a simmer in a medium saucepan over medium-high heat. Pour over the pork and vegetables. Nestle star anise pod (or aniseed) and cinnamon stick into the stew. Cover and cook until the pork and vegetables are tender, 3 to 3 1/2 hours on high or 5 1/2 to 6 hours on low.
Step 2
Discard the star anise pod and cinnamon stick. Skim or blot any visible fat from the surface of the stew. Add the cornstarch mixture, cover and cook on high, stirring 2 or 3 times, until slightly thickened, 10 to 15 minutes. Serve sprinkled with scallion greens and sesame seeds.