Sardi's opened in the theater district in New York City in 1927. It has been the requisite site since 1947 for Broadway actors, producers and directors to gather after opening night while they await reviews to come in. Back then, and even today, restaurant patrons dine among luxurious leather decor and reminisce over hundreds of caricatures of famous Broadway luminaries that decorate the restaurant's walls. Sardi's is quite well known for its many signature dishes that were created by its talented chefs, such as Shrimp Sardi (a particular popular dish that's still on their menu even today).
In a medium-size saucepan, heat 6 tablespoons of olive oil over medium-low heat. Add the onion, carrot, celery, and 1 garlic cover, and cook, stirring occasionally, until softened, about 10 minutes.
Add the shrimp shells and wine, bring to a boil, and simmer until reduced by half, about 4 to 6 minutes. Add the chicken broth, tomato, thyme, bay leaf, parsley, tarragon, tomato paste, salt, and pepper (to taste). Bring to a boil, reduce the heat to a simmer, cover, and cook for 20 minutes.
Strain the shrimp sauce through a sieve, pressing as much of the liquid from the solids as possible with the back of a wooden spoon. Add the crushed red pepper to the sauce. Then add the butter, incorporating it into the sauce 1 tablespoon at a time. Set aside.
Heat a large sauté pan over high heat, and add the remaining 2 tablespoons olive oil. Season shrimp with salt and pepper to taste, and sauté them quickly until just done, 2 to 3 minutes. Quickly add the remaining 4 garlic cloves and cook, stirring over medium heat for 1 minute. Stir the shrimp into the sauce. Sprinkle with chives, and serve with the toast alongside.
At Sardi's, this dish is usually served over cooked white rice.