Heat olive oil in a heavy-based pan over medium heat.
Fry shallots gently for 4 minutes until softened.
Add vermouth and fish stock, bring to a boil, then simmer for 20 minutes until syrupy.
Stir in cream, return to a boil, and simmer for 8 minutes until thickened.
Strain sauce through a sieve and stir in mustard and dill.
Preheat the oven to 200°C.
Prise the scallop shells apart with a thin knife.
Scoop the scallop meat from the shells using a spoon.
Clean scallops and separate the white meat from the skirt and roe.
Pat scallops and four shells dry, then halve scallops horizontally.
Sauté carrot and leek in vegetable oil until softened and let cool.
Spoon vegetables into shells, top with four scallop pieces, and add three tablespoons of sauce.
Roll puff pastry to 0.5cm thickness and cut into four thin strips.
Wrap one pastry strip around the join of each pair of shells to seal.
Brush pastry with egg yolk and bake for 10 minutes until golden.
Serve shells on sea salt or seaweed and cut pastry seals to open.