Melt 2 tablespoons butter in large Dutch oven or pot over medium heat. Add reserved shrimp shells (from 1 pound shrimp) and cook until spotty brown, about 5 minutes. Stir in ½ cup celery, ½ cup carrot and ½ cup shallot; season with salt and cook until beginning to soften, 5 minutes.
Stir in 2 tablespoons flour and cook, stirring constantly, until lightly browned, about 2 minutes. Stir in 2 tablespoons tomato paste, 4 thyme sprigs, and 2 dried bay leaves; cook for 1 minute. Deglaze with ½ cup vermouth, scraping up any browned bits; cook 1 minute.
Add 2 (8-ounce) bottles clam juice and ½ cup water; bring to a boil then reduce heat to medium and simmer until thickened, about 15 minutes.
Transfer reduced mixture to blender, add 1 cup milk and blend until completely smooth, at least 1 minute.
Pour soup through fine-mesh strainer back into Dutch oven or large pot, pressing on solids to extract soup. Discard solids.
Stir in remaining 1 ½ cups milk; bring soup to simmer over medium heat. Stir in 1 pound diced shrimp and ½ teaspoon Tabasco, if using, and simmer until shrimp are cooked through, 2–3 minutes.
Season with additional salt and Tabasco to taste. Serve with chives, Tabasco and/or red pepper flakes.