Cut lobster shell down the middle, crack it open, and pull out the meat. Cut the shell into 1-inch pieces and set aside.

Cut the meat into 1/2-inch pieces, removing any veins or shell fragments. Refrigerate until needed.

Melt 1 tablespoon butter in saucepan. Add lobster shells and cook until red (3-4 minutes). Add sherry and clam juice; simmer gently (15-20 minutes). Strain broth to remove shells.

Rinse saucepan and melt remaining butter. Cook diced carrots, celery, paprika, tomato paste, salt, pepper, and cayenne for 2 minutes. Stir in flour and cook for 1-2 minutes. Stir in lobster broth and bring to simmer.

Add cubed potatoes and gently simmer 10-15 minutes until tender and liquid slightly reduced.

Cut 3.5-inch puff pastry circles, brush with egg wash, and refrigerate.

Preheat oven to 425°F (220°C) and line baking sheet with foil.

Stir lemon juice, cream, and tarragon into potato mixture. Simmer for 5 minutes until thickened slightly.

Stir reserved lobster meat into pot and remove from heat. Divide mixture between two ramekins, leaving 1/4-inch space to the rim.

Place puff pastry over ramekins, ensuring vents are cut through. Bake for 20 minutes until browned on top.