Place a rack in the center of your oven and preheat the oven to 400 degrees F. Line a rimmed baking sheet with parchment paper. Leave the salmon in the refrigerator.

Heat the oil in a large, nonstick skillet. Add the spinach in large handfuls, cooking until it wilts, about 1 minute. Stir in the garlic, thyme, remaining 1/2 teaspoon salt and ¼ teaspoon pepper. Stir in the Parmesan. Remove from the heat and let cool.

Place the puff pastry on a lightly floured work surface and roll it into a 12x14-inch rectangle. With a sharp knife, cut the puff pastry in half crosswise so you are left with two rectangles that are 12 x 7 inches each.

Remove the salmon fillets from the refrigerator and place on a plate. Brush the tops of the fillets liberally with the butter mixture, then place each fillet, butter-side down, in the center of a piece of puff pastry. Spoon half of the cooled vegetables over the top.

Fold one side of the puff pastry over the top of the fillet like a flap, so that it partially covers it, then brush the top of the flap with egg wash. Fold the next side, adhering it to the first if the flaps are large enough to touch (the egg wash should act as a “glue”), then brush its top with egg wash. Repeat until all 4 sides are folded over. It should be as if you are wrapping up the salmon like a delicious present. Don’t stress over the order of the flaps. As long as it’s well sealed and covers the salmon, you’re golden. Carefully flip the salmon over and transfer it to the prepared baking sheet, with the folded side underneath. Repeat with the second fillet.

Brush the tops of the puff pastry with egg wash, then with a sharp knife, score shallow, diagonal lines in each direction in a crosshatch pattern.

Bake the salmon for 20 to 25 minutes, or until the pastry turns golden brown. Let cool a few minutes on the baking sheet. Serve hot.