Step 1In a medium, heavy-bottom saucepan, bring the milk and sugar just to a boil over high heat, stirring occasionally. Remove from the heat and pour into a metal bowl set over a bowl of ice water. Stir until the sweetened milk is thoroughly chilled.
Step 2Pour the coconut puree, lime juice and zest into a blender (or use an immersion blender and large bowl); pulse to combine. Add the sweetened milk and pulse several more times to combine.
Step 3Place the mixture in an ice cream maker and freeze according to the manufacturer's instructions. Cover tightly with plastic wrap and keep frozen until needed. This makes a generous quart of sorbet, slightly more than is needed for the coupe recipe. The remainder will keep, tightly covered and frozen, for 1 week.