Preheat the oven to 180°c (fan-assisted).
Melt the butter in a large heavy-bottomed pan over a medium heat. Add the sliced leeks and a good pinch of salt and cook, stirring regularly, for 12-15 minutes, or until they have collapsed and are starting to brown. Finish with a few good grinds of black pepper, then taste and adjust the seasoning, if needed.
Meanwhile, lay the pastry, still on its baking parchment, onto a baking tray. Use a knife to indent a ½ inch border all the way round the pastry, then brush with some of the leftover egg whites and bake for 10 minutes.
Combine the egg yolks, crème fraîche, mustard and a good pinch of salt and black pepper in a bowl. Set to one side until you are ready to build the tart.
Sprinkle the grated Gruyère evenly over the base of the par-cooked pastry, leaving the border clear. Top with the leeks, then pour the crème fraîche mixture over them. The mixture is quite fluid, so aim for the centre; the leeks will help keep it from running over the sides - though, if it does, don't worry. It may look a little rustic, but it will taste great. Bake for a further 18-22 minutes, or until the pastry is puffed, golden and cooked through. Let it cool for 5 minutes.
Grate a lot of Parmesan over the top, more than you think. It should be covered with Parmesan! Finish with a crack of black pepper, then slice into squares, and eat warm.
