Heat butter and sugar together in a heavy saucepan over low heat until mixture turns light brown, about 5 minutes. Add nectarine quarters and cardamom pods; cook and stir over medium heat until nectarines are soft, about 18 minutes. Remove and discard cardamom.
Remove saucepan from heat and allow nectarine mixture to cool slightly. Transfer mixture to a blender or food processor and blend until smooth; place in the refrigerator until completely cooled, about 30 minutes.
Beat double cream in a glass, metal, or ceramic bowl until soft peaks form. Lift your beater or whisk straight up: the cream will form soft mounds. Spoon cream over chilled compote.