Combine the blackberries, sugar, lemon peel, and 1 cup water in a small saucepan. Bring to a boil, reduce heat, and simmer until berries have fallen apart and juices are syrupy, 15 to 20 minutes. Strain through a fine-mesh strainer, pushing on solids to extract all the liquid. (Makes 1 cup). Let cool.
Divide syrup and ice cream between 4 tall glasses. Top with ginger beer.