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1
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.
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2
Remove from heat and let steep, covered, 25 minutes.
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3
Sprinkle gelatin over water and lime juice in a bowl and let soften 1 minute.
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4
Return cream mixture to a simmer, then pour through a very fine sieve into gelatin, pressing on and discarding solids.
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5
Stir until gelatin is dissolved, about 1 minute.
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6
Gradually add yogurt, whisking, and chill, covered, 30 minutes.
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7
(Mixture will not be gelled.)
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8
Beat remaining 1/3 cup cream in a chilled bowl with whisk until it just holds soft peaks.
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9
Fold into yogurt mixture and chill, covered, at least 8 hours.
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10
(Mousse will be softly set.)
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11
Blend honeydew, Midori, lime juice, and a pinch of salt in a blender at high speed until smooth, about 1 minute.
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12
Pour through a fine sieve lined with dampened cheesecloth into a bowl.
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13
Let drain, undisturbed, 30 minutes, then discard foam remaining in cheesecloth.
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14
Sprinkle gelatin over water in a small saucepan and let soften 1 minute.
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15
Add 2 tablespoons melon juice and sugar, then cook over low heat, stirring, until gelatin and sugar are dissolved, 1 to 2 minutes.
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16
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.
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17
(Honeydew water will be barely set.)
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18
Spoon honeydew water onto 4 dessert plates and top with shiso leaves.
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19
Spoon mousse onto leaves.
