Add the seafood stock, lobster shells, potatoes, carrots and thyme to a large stockpot. Season with salt and pepper. Bring to a boil, reduce to a simmer and cook until the potatoes and carrots are tender, about 10 minutes. Remove the lobster shells and thyme sprigs, strain the stock and reserve the vegetables in a separate bowl.
Add the butter and oil to the stockpot over medium heat. Add the lobster meat and cook until just beginning to turn red and opaque, about 2 minutes. Remove the meat and reserve. Add the celery, onions, salt and a few cracks of black pepper and cook until translucent and softened, about 5 minutes. Stir in the flour, cooking for about 3 minutes, and then stir in the tomato paste and cook for another minute. Slowly pour in the sherry, whisking to combine. Bring to a simmer and reduce by half, about 5 minutes. Add the reserved lobster stock and bring to a simmer until the liquid has thickened. Add the reserved vegetables and peas. Stir in the cream and lobster meat. Taste and season with salt and pepper as needed.
Preheat the oven to 425 degrees F.
Divide the filling between four 16-ounce ramekins. Beat together the egg and 1 tablespoon water in a small bowl. Dust the counter and a rolling pin with flour and roll out the puff pastry sheets. Cut 4 rounds big enough to cover the tops of the ramekins. Pierce the centers with a sharp knife to create 2 small slits. Brush the outside of the ramekins with egg wash and then top each with a puff pastry round, pressing gently to seal around the edges. Brush the top with egg wash. Bake until the tops are puffed and golden, 20 to 25 minutes.