Peel and devein shrimp; reserve shells. In a medium saucepan, add shells to seafood stock. Bring to a boil and simmer 10 minutes. Discard shells, set enriched stock aside.
In a Dutch oven, melt 2 tablespoons butter over medium heat. Add shrimp and garlic and cook, stirring often, until shrimp are just pink and firm. Do not over cook. Transfer the shrimp to a bowl and set aside.
Melt remaining butter in pot and add shallots. Cook until soft and aromatic, about 2 minutes. Add the dry sherry and allow it to come to a boil. Reduce the liquid until it is a glaze and the pan is nearly dry.
Remove the pan from the heat and quickly add the brandy, the return to heat. Be careful, the brandy may ignite. If it does, cover the pan with 1 minute to put out the flame.
Add the seafood stock and bring to a boil. Reduce, stirring often, until it is a thick glaze, about 10 minutes. Add heavy cream and Dijon mustard and stir until well combined. Reduce the heat to low and add Worcestershire sauce and shrimp, stirring to coat. Cook, stirring often until the sauce is bubbling and the shrimp are heat through, about 2 minutes.
Season with salt and pepper to taste. Serve over cooked pasta and garnish with chives.