1. Place a 2-quart shallow baking dish in the freezer. In a medium saucepan, bring sugar and orange juice to a boil over medium-high heat, stirring, until sugar dissolves, about 2 minutes. Remove from heat. Stir in cranberry and lemon juice, zest, and a pinch of salt.

2. In a fine-mesh strainer set over cranberry mixture, press ginger with a spoon to release juice (discard solids). Stir to combine.

3. Pour mixture into baking dish. Freeze until solid, at least 6 hours or overnight. Mash with a fork to break granita into small crystals. Cover; freeze until ready to serve.