Whisk all ingredients except Satsuma Swirl to combine, then refrigerate for at least 2 hours.
Place ice cream base in ice cream maker and follow manufacturer’s instructions.
When mixture is finished freezing, place one third of mixture in freezer safe container and add layer of swirl, add another third of mixture and more swirl, until container is filled.
Cover and place in freezer for 2 hours.
Place satsumas in blender and purée to fine pulp, about 20 seconds.
Pour orange purée and water into small pan and bring to boil. Once mixture is bubbling, add sugar and stir well. Reduce heat and simmer until reduced by half, about 30 to 45 minutes. Stir occasionally. Remove from heat and cool completely.