Spread 2 full sheets frozen puff pastry out on clean, flat work surface. Leave room between sheets to work with each individually.
Remove 2 6-ounce boneless, skinless salmon fillets from refrigerator. Pat fillets completely dry on all sides with paper towels, then place 1 fillet off-center on each pastry sheet. Leave approximately 2 to 3 inches of pastry exposed above, below, and to one side of each salmon fillet.
Season top of each salmon fillet with salt and freshly cracked black pepper to taste. Spoon half of spinach filling on top of each salmon fillet, spreading filling out to cover fillet as evenly as possible.
Take edge of puff pastry opposite salmon fillet and fold pastry over to cover salmon, as if closing books. Carefully pinch, crimp, or roll edges of puff pastry completely closed, fully encasing salmon and filling in pastry sheet. Repeat with remaining pastry sheet.
Once each puff pastry sheet is wrapped and sealed around each salmon fillet, carefully transfer both to prepared baking sheet. Leave room between each Salmon Wellington to allow for any pastry expansion.
Crack 1 large egg into small bowl. Whisk egg vigorously until well beaten with no streaks remaining.
Use paring knife to lightly score tops of each Wellington in crosshatch pattern, being careful not to cut completely through pastry sheet and into filling. Once pastries are scored, lightly brush tops of pastries with beaten egg.