Place the cranberries into a saucepan and fill with just enough water so that they are floating slightly. Bring to a boil and cook until the cranberries pop. Remove from the heat and pour off any excess water. Run through a food mill, or strain back into the saucepan. Stir in the sugar and cook over low heat just long enough to dissolve the sugar. Transfer to a bowl and refrigerate until cold.
When the cranberry mixture is cold, stir in the milk and heavy cream. Pour into an ice cream maker and freeze according to the manufacturer's instructions.