Cook the leeks with a knob of butter until tender. Cool slightly, season well and stir in the cream and half the egg.
Heat the oven to 390F/gas 6/fan 350F. Cut the pastry into 4. Cut a diagonal slit about 0.2 inches into each corner, then fold over each edge to make a narrow border.
Divide the leek mix between the pastries and top with grated Beemster goat's cheese. Glaze the edges of the pastry with the rest of the egg, then bake for 25 minutes until golden and crisp.