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1
In a blender, combine the cucumber, avocados, buttermilk, vinegar, sugar, 1/2 tablespoon of the lime juice and a pinch of salt.
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2
Blend until smooth.
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3
Strain the soup through a fine sieve and refrigerate until chilled, about 40 minutes.
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4
In a large saucepan, heat 2 tablespoons of the olive oil.
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5
Add the shrimp shells, garlic, shallot and carrot and cook over moderate heat, stirring until the shells are lightly browned, and the vegetables are softened, about 8 minutes.
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6
Add the peppercorns, coriander seeds, crushed red pepper and cumin seeds and cook, stirring, for 1 minute.
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7
Add the tomato paste and cook, stirring, for 1 minute.
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8
Add the water, honey and remaining 1 tablespoon of lime juice and bring to a boil.
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9
Simmer over moderate heat until reduced to 1/2 cup, about 15 minutes.
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10
Strain the shrimp sauce into a heatproof bowl.
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11
In a medium skillet, heat the remaining 1 tablespoon of olive oil until shimmering.
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12
Add the shrimp, season with salt and pepper and cook over high heat for 1 minute.
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13
Turn the shrimp, add the shrimp sauce and simmer just until the shrimp are cooked through, about 2 minutes.
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14
Swirl in the butter.
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15
Place the shrimp in soup bowls, spoon the cucumber soup all around and drizzle the shrimp sauce on top.
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16
Sprinkle with the mint and serve right away.
