Preheat the oven to 400 degrees F and line a rimmed baking sheet with parchment paper. Keep the salmon in the refrigerator.

Melt the butter in a small bowl or saucepan. Stir in the Dijon, lemon zest, ¼ teaspoon kosher salt, and ¼ teaspoon black pepper. Set aside.

Heat the oil in a large, nonstick skillet. Add the spinach and cook until it wilts, about 1 minute. Stir in the garlic, thyme, remaining ½ teaspoon salt, and ¼ teaspoon pepper. Stir in the Parmesan and let cool.

In a small bowl, lightly beat the egg yolk with 1 teaspoon water for the egg wash. Set aside.

Roll the puff pastry on a lightly floured surface into a 12×14-inch rectangle. Cut the puff pastry in half crosswise into two 12 x 7-inch rectangles.

Remove the salmon fillets from the refrigerator, brush the tops with the butter mixture, and place each fillet, butter-side down, in the center of each puff pastry rectangle. Spoon half of the cooled spinach mixture over each fillet.

Fold one side of the puff pastry over the fillet, brushing the top with egg wash, then fold the next side and brush with egg wash again. Repeat until all four sides are folded over. Carefully flip and transfer to the prepared baking sheet, folded side underneath. Repeat with the second fillet.

Brush the tops of the puff pastry with egg wash and score the pastry with diagonal lines in a crosshatch pattern.

Bake the salmon for 20 to 25 minutes, or until the pastry turns golden brown. Let cool for a few minutes before serving hot.