Heat oven to 190C/fan 170C/gas 5. Roll out the pastry and line a shallow 28cm flan tin. Trim off the edges, then line with baking paper and beans. Put on a baking sheet, bake for 10 mins. Remove the paper and beans, then bake for 5 mins more.
Cook the potatoes in boiling salted water for 6-8 mins until tender, then drain. Beat together the cream, eggs, dill, lime zest, salt and pepper. Scatter half the potatoes over the bottom of the pastry case, then put half the salmon strips in the gaps. Pour over half the egg mix, then arrange the remaining potatoes over the salmon pieces and put the remaining salmon in the gaps between. Pour over the rest of the egg mix.
Bake for 25 mins until the top is lightly coloured and firm to the touch. Cool for 10 mins before removing from the tin, then serve warm or at room temperature sprinkled with extra dill.