Sataejjim (Slow Cooker Braised Beef Shank)

Name: Sataejjim (Slow Cooker Braised Beef Shank)
Cuisine: Asian, Korean
Ingredients: 3 pounds beef shank meat (satae, 사태); 10 ounces root vegetables (parsnip, celery root, burdock root, turnip, and/or Korean radish); 1 medium carrot; 1/2 medium onion; 2 scallions; 8 plump garlic cloves; 3 to 4 thin ginger slices (about 1-inch round); 4 dried shiitake mushrooms (or any other dried mushrooms, broken up into 2 to 3 pieces); 4 small dried red chili peppers (or 1 teaspoon crushed red peppers - optional); ⅓ cup soy sauce; 1/4 cup rice wine (or dry white wine); 2 tablespoons apricot preserve (or honey - see note); 1 tablespoon sugar; pepper to taste; salt; 1 tablespoon sesame oil; 1 scallion (roughly chopped)