Empty cranberries into a saucepan and transfer 1/2 cup to a small bowl.

Add sugar, zest, and water to pan and cook over low heat, stirring occasionally until sugar dissolves (about 10 minutes).

Increase heat to medium and cook until berries burst (about 12 minutes).

Reduce to low and stir in reserved cranberries. Add sugar, salt, and pepper to taste.

Cool to room temperature before serving.