1. Poach the salmon in the hot fish stock and white wine for 10 minutes. Drain.
2. Cook the rice in the salmon cooking stock for about 20 minutes, and boil the spinach in salted water for 20 minutes as well.
3. Sauté the chopped shallots and mushrooms in the hot butter. Season with salt, pepper, and a squeeze of lemon juice. Let cool.
4. Drain the rice and spinach well. Flake the salmon. Peel and crush the hard-boiled eggs.
5. Chop the dill and chives.
6. Roll out 2/3 of the pastry into a thick rectangle. Spread the rice, then the flaked salmon, dill, shallot mushrooms, chives, and finally the hard-boiled eggs on top. Make sure to leave a 2 cm border of pastry on each side.
7. Fold up the edges, then cover with the remaining rolled-out pastry in an equally sized rectangle. Seal the edges by pinching or creating a sort of hem.
8. Decorate the top by scoring with a knife. Brush with a mixture of beaten egg yolk and milk.
9. Bake the koulibiac in the oven at 210°C (thermostat 7) for 20 minutes. Serve hot or warm, with a tomato coulis.