01 - Combine water and sugar in a small saucepan. Bring to a gentle simmer over medium heat, stirring constantly until sugar completely dissolves. Remove from heat immediately.
02 - Add fresh basil leaves to the hot syrup, pressing lightly with a spoon to release their aromatic oils. Cover and let steep for 10 minutes to extract flavor.
03 - Pour the syrup through a fine mesh strainer into a clean mixing bowl. Discard the used basil leaves.
04 - Whisk the freshly squeezed pink grapefruit juice, grapefruit zest, and lemon juice (if using) into the basil-infused syrup until fully incorporated.
05 - Cover the bowl and refrigerate for at least 1 hour until the mixture is thoroughly chilled, preferably overnight for deeper flavor development.
06 - Pour the cold mixture into an ice cream maker and churn according to manufacturer's instructions, typically 20–25 minutes, until the sorbet reaches a soft-serve consistency.
07 - Transfer the churned sorbet to a freezer-safe container. Cover tightly and freeze for at least 3 hours until firm enough to scoop.
08 - Let the sorbet sit at room temperature for 5 minutes before serving to soften slightly. Scoop into chilled bowls or glasses and serve immediately.