01 - Combine water and sugar in a small saucepan. Bring to a gentle simmer over medium heat, stirring until sugar completely dissolves. Remove from heat.
02 - Add basil leaves to the hot syrup, pressing lightly with a spoon to release their flavor. Cover and steep for 10 minutes.
03 - Strain the syrup into a mixing bowl, discarding the basil leaves.
04 - Add pink grapefruit juice, grapefruit zest, and lemon juice if desired to the basil-infused syrup. Stir well to combine.
05 - Cover and refrigerate for at least 1 hour until thoroughly chilled.
06 - Pour chilled mixture into an ice cream maker and churn according to manufacturer's instructions, typically 20–25 minutes, until reaching soft-serve consistency.
07 - Transfer sorbet to a freezer-safe container, cover, and freeze for at least 3 hours until firm.
08 - Let sorbet sit at room temperature for 5 minutes before serving to soften slightly. Scoop and serve immediately.