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using a sharp paring knife, peel the oranges, removing the skin and all the bitter white pith. Working over a bowl to catch the juice, cut in between the membranes to release the sections. Reserve the orange sections and juice in separate bowls.
In a nonreactive medium saucepan, combine the cranberries with the sugar and 1/4 cup of the reserved orange juice. Cook over low heat, stirring often, until the cranberries pop and soften, about 4 minutes. Remove from the heat and stir in the orange sections and Grand Marnier. Refrigerate the compote until cool.