Use a microplane to grate just the orange part of the orange peel, and set aside. Juice the oranges; you need a cup and a half. Set juice aside to chill.

Put the cranberries in a saucepan with the grated orange peel, sugar, water, and thyme. Partially cover the pan and boil until most of the cranberries pop, about seven minutes. Pour the mixture into a food mill*, and process to extract as much juice and pulp as you can, leaving the skins and thyme behind. Refrig­erate the strained mixture until thoroughly chilled.

Stir in the orange juice. Freeze in an ice cream maker according to the manufacturer‘s directions.

No food mill? No worries. Pour the mixture into a fine sieve set on top of a deep bowl; stir and press down on the fruit with the back of a large spoon.