Unroll the pizza dough and divide light brown sugar and cinnamon evenly over top.
Place the cranberries in a food processor and pulse until finely chopped. Evenly disperse over sugar.
Roll the dough up, starting from the edge closest to you and pinching edges together at the end. Slice dough into 12 rolls.
Place the rolls in a lightly-greased pan. Either bake for 25 minutes, until golden brown and cooked through, or freeze. To freeze the rolls, wrap the pan in two layers of plastic wrap and bake within 2 weeks.
Combine sugar, zest and juice in a small bowl. Stir with a whisk until well combined. If the icing seems too runny, whisk in a bit more sugar until you reach a desired consistency.
Let the rolls rest for 10 minutes before glazing and serving.