Preheat the oven to Fan 180˚C/ Gas mark 6 / 400˚F.
First make the pastry. In a large bowl, rub the butter into the flour until it resembles fine breadcrumbs. Add the salt and mix in the eggs along with the water, bringing it together to form a dough. Gently knead for 30 seconds and roll into a cylinder. Now gently roll out the pastry onto a lightly floured surface, big enough to line a 23cm pastry ring (ring depth at least 4cm). Grease the ring with butter, then carefully fold the pastry circle into four making a triangle. Put the corner in the centre of the ring then carefully unfold the pastry making sure you get the pastry into the sides. Put into the fridge for 20 minutes until chilled.
Remove from the fridge and prick the base of the pastry with a fork. Crumple up a sheet of parchment and place into pastry case making sure the paper is pushed into the edges of the base. Fill to the top with rice. Bake for 20 minutes, then remove from the oven, removing the crumpled parchment and rice. Return to the oven and bake for a further 5 minutes. Remove and leave to cool, then using a sharp knife, cut off the excess pastry.
For the filling, put the salmon fillets into an oven proof dish covered with tin foil. Bake in the preheated oven for 10 minutes. Leave to rest for at least 10 minutes.
In a large bowl whisk together the egg yolks and whole eggs, season with salt and pepper and a pinch of cayenne, fold in the double cream.
Scatter pieces of the salmon into the base of the pastry, sprinkle with tarragon and top with the egg mixture. Bake in the oven for approximately 45 minutes, turning down the heat after 30 minutes to Fan 150˚C/ Gas mark 3 / 325˚F. If the centre is still soft, continue cooking for another 5 minutes. Allow to rest on a wire rack for 20 minutes before slicing.