2 tablespoons fresh lime juice plus 1/2 teaspoon finely grated lime zest
1 cup water
2 large freestone peaches, cut into wedges
Bring a small saucepan of water to a boil and fill a small bowl with ice water. Add the basil to the saucepan and blanch for 10 seconds. Drain and immediately transfer to the ice water to cool. Drain, gently squeezing out the excess water.
Transfer the basil to a blender. Add the sugar, lime juice, lime zest and water and puree until smooth, about 1 minute. Strain the liquid through a fine sieve and transfer to an ice cream maker. Process according to the manufacturer's instructions, about 15 to 20 minutes. Transfer the ice to a shallow dish and freeze until just firm enough to scoop, about 10 minutes.
Scoop the basil-lime ice into 4 bowls. Top with the peach wedges and serve immediately.