Connecticut Cajun Shrimp Rolls

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1 cup red wine vinegar

1 tablespoon plus 1 teaspoon Cajun seasoning

1 tablespoon black peppercorns

4 medium carrots, chopped

2 celery stalks, chopped

1 head of garlic, halved crosswise

5 bay leaves

5 sprigs fresh thyme

Kosher salt

1 pound medium shrimp, shell-on

6 tablespoons (3/4 stick) unsalted butter

4 split-top hot dog buns

2 tablespoons minced fresh chives

Lettuce leaves, for serving