Combine cider, cinnamon stick, clove, orange slice, and lemon slice in a medium saucepan; bring to a boil. Cover, reduce heat, and simmer 30 minutes. Strain cider mixture through a sieve into a bowl; discard solids. Serve warm. Garnish each serving with 1 cinnamon stick, if desired.
Simple Cranberry Sauce
Serves 14 - 2 tablespoons per serving
1/2 cup packed dark brown sugar
1/2 cup orange juice
1/4 cup water
1 1/2 tablespoons honey
1/8 teaspoon ground allspice
1 - 12 ounce bag fresh cranberries
1 - 3 inch cinnamon stick
Combine all ingredients in a medium saucepan over medium-high heat; bring to a boil. Reduce heat, and simmer 12 minutes or until mixture is slightly thickened, stirring occasionally. Discard cinnamon stick; cool completely.
COOK'S NOTE: You can make up to two days ahead and refrigerate.