1. Preheat oven to 425 degrees Fahrenheit.
2. Drizzle some olive oil into a large saute pan over medium-high heat. Add the sliced leek and salt to taste. Saute for a few minutes until leeks are translucent, and then add garlic.
3. In the meantime, add mushrooms and the leaves of one sprig of thyme to a food processor. Pulse until it resembles coarse crumbs (not too fine). Add this mixture to the leeks in the pan (if too dry, add more olive oil) and season with a sprinkle of salt. When the vegetables are softened, remove from the fire and transfer to a bowl.
4. On a clean work surface, lightly roll out the sheet of puff pastry and cut into four squares. Spread a tablespoon of Dijon mustard on each square. Place a few leaves of baby spinach on top of the Dijon.
5. Season the salmon fillets with salt, pepper, and a drizzle of olive oil. Pack some of the mushroom-leek mixture on top of each fillet, and then invert the fish over the spinach (the fillet should now be upside down).
6. Wrap the puff pastry over the fish, turn it over, brush with the beaten egg, and make a small slit in the pastry dough. Sprinkle with coarse salt and thyme. Place on a greased aluminum baking sheet and bake for 20 minutes until golden brown.