- 3/4 cup sugar
- 1/4 cup water
- 1 teaspoon finely grated fresh lemon zest
- 5 cups coarsely chopped seeded watermelon (from a 4-lb piece, rind discarded)
- 2 tablespoons fresh lemon juice, or to taste
- 1/4 cup packed fresh basil leaves
- 1 1/2 cups dry white wine
- 1/2 cup sugar
- 1 teaspoon finely grated fresh lemon zest
- 1/2 cup plus 2 tablespoons water
- 2 teaspoons unflavored gelatin (from 1 envelope)
- 2 tablespoons fresh lemon juice, or to taste
- Special equipment: an ice cream maker
- Bring sugar, water, and zest to a boil in a 2-quart heavy saucepan, stirring until sugar is dissolved, then reduce heat and simmer, without stirring, washing down any sugar crystals on side of pan with a pastry brush dipped in cold water, 2 minutes.
- Put watermelon in a blender, then add syrup and lemon juice and blend until smooth. Pour through a fine-mesh sieve into a large bowl, pressing on pulp and discarding any remaining solids.
- Freeze in ice cream maker, then transfer to an airtight container and freeze until firm.
- Blanch basil in a 3-quart pot of boiling salted water 5 seconds, then drain and transfer to a bowl of ice and cold water to stop cooking. Drain basil and squeeze dry.
- Bring wine, sugar, zest, and 1/2 cup water to a boil in cleaned 2-quart heavy saucepan, stirring until sugar is dissolved, then simmer 2 minutes.
- While wine syrup simmers, sprinkle gelatin over remaining 2 tablespoons water in a large metal bowl and let soften 1 minute.
- Pour about 1/2 cup wine syrup through a medium-mesh sieve lined with a dampened paper towel into gelatin mixture (reserve lined sieve), then stir until gelatin is dissolved.
- Blend remaining syrup with basil and lemon juice in cleaned blender until smooth (use caution when blending hot liquids), then pour through lined sieve into gelatin mixture. Set bowl in a larger bowl of ice and cold water and let stand, stirring occasionally, until cold, about 15 minutes, then chill in refrigerator, uncovered, until set, at least 2 hours.
- Gently whisk gelée to break into small pieces and serve as a bed for scoops of sorbet.