If using Seville oranges, grate the zest of 2 of them. Squeeze the juice of all 3 and pour into a bowl with the zest and sugar. If you're going for the sweet orange and lime option, grate the zest of the orange and 1 of the limes, juice them and add to the sugar as before. Stir to dissolve the sugar and add the heavy cream.
Whip everything until it holds soft peaks, and then turn into a shallow airtight container (approximately 2-quarts) with a lid. Cover and freeze until firm (from 3 to 5 hours). Remove to ripen for 15 to 20 minutes (or 30 to 40 minutes in the refrigerator) before eating. Serve in bowl, in cones, with wafers - however you like.