Peel and devein the shrimp, reserving half of the shrimp heads and all of the peels for making the soup. (Discard remaining heads.) Reserve peeled and deveined shrimp separately, refrigerated, until ready to serve the soup.

Set a deep, wide pot over medium-high heat and add the olive oil. Once the oil is hot, add the onions, carrots and celery. Saute, stirring, until the vegetables are lightly caramelized, about 7 to 8 minutes. Add the shallots, leeks and garlic and saute, stirring occasionally for 1 minute. Add the tomato paste to the pan and cook until the vegetables are well coated about 2 to 3 minutes. Add the reserved shrimp shells and heads to the pan and cook until the shells are pink and well caramelized, about 5 minutes. Add the chicken broth, bay leaf and thyme and bring to a boil then reduce to a simmer. Season with 2 teaspoons salt, 1/2 teaspoon white pepper and the paprika, simmer about 45 minutes. In a clean pot large enough to hold the stock, combine 4 tablespoons of butter with 4 tablespoons of flour to form a roux. Strain the finished stock through a fine mesh sieve into the roux. Add the heavy cream, brandy and cayenne pepper and return to a simmer. Add sherry vinegar and lemon juice to taste and adjust the seasoning if necessary. Add the reserved shrimp, stir to combine, then cook until shrimp are just cooked through, 1 to 2 minutes. Garnish with chopped chives and serve immediately.