In a small saucepan over medium heat, combine 3/4 cup satsuma juice, sugar, and salt. Heat until sugar dissolves, stirring occasionally. Remove from heat and pour into a medium bowl. Zest satsumas directly over the bowl. Stir in remaining satsuma juice, triple sec, milk, and cream. Whisk to combine.
Cover bowl and place sherbet base in the refrigerator to fully chill. Once chilled, pour into an ice cream maker and freeze according to the manufacturer’s instructions. My sherbet took 20 minutes to get to my desired consistency. Place plastic or parchment over sherbet (to prevent ice crystals) and freeze until firm, at least 4 hours. Recipe adapted from Scoop Adventures, Satsuma Sherbet.