Put the vinegar, 1 tablespoon Cajun seasoning, peppercorns, carrots, celery, garlic, bay leaves, thyme and 1 teaspoon salt in a medium saucepan and cover with 6 cups water. Bring to a boil over high heat, then reduce the heat and simmer for about 15 minutes. Scoop out the solids with a strainer and discard (or save the bigger veggies for adding to salads). Reserve the poaching liquid.
Bring the poaching liquid back to a simmer and add the shrimp. Poach until the shrimp are bright pink and just cooked through, about 2 minutes. Use a slotted spoon to transfer the shrimp to a plate and then refrigerate until cool enough to handle. Peel and devein the shrimp and coarsely chop.
Melt the butter and remaining 1 teaspoon Cajun seasoning in a large skillet over medium heat. Brush the cut sides of the buns with some of the butter and toast in the skillet, buttered side down, until golden, 1 to 2 minutes.
Toss the shrimp with the chives and season with salt. Divide the lettuce and shrimp among the buns, drizzling with any remaining butter. Serve warm.
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