- 2/3 cup chilled heavy cream
- 1/4 cup sugar
- 3 (2- by 1 1/4-inch) fresh or frozen kaffir lime leaves
- 1 1/2 teaspoons finely grated fresh lime zest
- 3/4 teaspoon unflavored gelatin (from a 1/4-ounce envelope)
- 1 tablespoon water
- 1/2 teaspoon fresh lime juice
- 1 cup plain whole-milk yogurt
- 3 cups (1-inch) pieces honeydew flesh (2 pounds)
- 2 tablespoons Midori (melon liqueur)
- 1 tablespoon fresh lime juice
- 1 teaspoon unflavored gelatin
- 1 tablespoon water
- 2 tablespoons sugar
- Garnish: 4 fresh green shiso leaves
- Accompaniment: chile lime tuiles
- Special equipment: cheesecloth
- Stir together 1/3 cup cream, sugar, lime leaves, zest, and a pinch of salt in a small heavy saucepan and bring to a bare simmer over moderately low heat, stirring until sugar is dissolved. Remove from heat and let steep, covered, 25 minutes.
- Sprinkle gelatin over water and lime juice in a bowl and let soften 1 minute. Return cream mixture to a simmer, then pour through a very fine sieve into gelatin, pressing on and discarding solids. Stir until gelatin is dissolved, about 1 minute. Gradually add yogurt, whisking, and chill, covered, 30 minutes. (Mixture will not be gelled.)
- Beat remaining 1/3 cup cream in a chilled bowl with whisk until it just holds soft peaks. Fold into yogurt mixture and chill, covered, at least 8 hours. (Mousse will be softly set.)
- Blend honeydew, Midori, lime juice, and a pinch of salt in a blender at high speed until smooth, about 1 minute. Pour through a fine sieve lined with dampened cheesecloth into a bowl. Let drain, undisturbed, 30 minutes, then discard foam remaining in cheesecloth.
- Sprinkle gelatin over water in a small saucepan and let soften 1 minute. Add 2 tablespoons melon juice and sugar, then cook over low heat, stirring, until gelatin and sugar are dissolved, 1 to 2 minutes. Gradually whisk in 1 1/8 cups melon juice (reserve remainder for another use if desired), then transfer to a bowl and chill, covered, at least 8 hours. (Honeydew water will be barely set.)
- Spoon honeydew water onto 4 dessert plates and top with shiso leaves. Spoon mousse onto leaves.