Combine cranberries, water, orange zest, orange juice, sugar and cinnamon stick (if using) in a medium saucepan. Bring to a boil over medium-high heat. Cook, stirring often, until the cranberries are tender and begin to pop, 3 to 5 minutes. Transfer to a large bowl. Cover loosely and refrigerate until thoroughly chilled, about 2 hours.

An hour or two before serving, prepare grapefruit: With a sharp knife, remove the skin and all the white pith from the fruit. Working over a bowl, cut the segments from their surrounding membranes. Squeeze juice from the membranes into the bowl before discarding. Add the segments and juice to the cranberry mixture. To serve, divide the compote among 6 dessert bowls and garnish with mint. Cranberry & Pear Variation: Instead of grapefruit, peel and core 3 to 4 Bartlett or Anjou pears; cut into 1/2-inch wedges. In Step 1, after the mixture comes to a boil, add pears and reduce heat to medium-low. Simmer gently until the cranberries and pears are tender, 5 to 10 minutes. Cover loosely and refrigerate until thoroughly chilled, about 2 hours. Omit Step 2.

MAKE AHEAD TIP: Cover and refrigerate for up to 2 days.