Connecticut Cajun Shrimp Rolls

Name: Connecticut Cajun Shrimp Rolls
Ingredients: 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