Remove the salmon fillets from the refrigerator and slice each in half crosswise. Pat dry with paper towels and set aside.
Preheat the oven to 400°F. Line a baking sheet with parchment paper.
To the bowl of a food processor, add the garlic, shallots, and mushrooms.
Pulse to mince everything.
In a skillet over medium heat, melt the butter. Add the mushroom mixture and cook until softened, approximately 3 minutes. Add the wine and cook until the wine has evaporated, about 2 more minutes.
Turn the heat off and stir in the crème fraiche and mustard. Season with salt and pepper and set aside to cool.
Lightly season the salmon fillets on both sides with pinches of salt and pepper.
Dust a flat work surface with a little flour. Place one unfolded sheet of puff pastry on the surface and lightly dust the top with a little more flour. Using a rolling pin, roll the pastry out to about an 8-inch x 12-inch rectangle. Cut the pastry sheet into 4 quarters. Do the same with another sheet of pastry.
Place equal amounts of spinach leaves in the center of 4 of the rectangles of pastry. Top each layer of spinach with a salmon fillet. Spoon 2 tablespoons of mushroom paste over each fillet.
In a small mixing bowl, whisk together the egg and water.
Brush the edges of each topped pastry sheet with some egg wash. Place another rectangle of pastry over the salmon fillets and seal the edges together with the tines of a fork. You want a good tight seal.
Transfer the filled puff pastry packets to the parchment-lined baking sheet with a spatula or bench scraper. Brush the tops of each packet with the remaining egg wash. Make 3 small slits in the top of each packet with a sharp paring knife.
Place the baking sheet inside the oven and bake for 15 minutes until the pastry is golden brown. Remove from the oven and allow the Wellingtons to rest for 5 minutes. Meanwhile, transfer the dill sauce to a small serving bowl with a spoon.
Arrange the salmon Wellington packets on individual serving plates with your favorite side dishes and sauce on the side. Serve while still warm.