Preheat Oven: Preheat oven to 400°F (200°C). Line a large baking sheet with parchment paper. This preparation ensures your pastries will cook evenly and won't stick to the baking sheet, making cleanup easier.
Prepare Pastry: Cut the puff pastry sheets into 5-inch (13cm) squares and place in the refrigerator until ready to use. Keeping the pastry cold helps maintain its flaky texture when baked.
Make Roux Base: Melt butter in a saucepan over medium heat. Add flour and kosher salt, cooking for 1 minute while stirring frequently. This creates a roux that will thicken your sauce and provide a smooth, velvety texture.
Create Béchamel: Slowly add milk while whisking constantly until the mixture is smooth and begins to boil. Continuous whisking prevents lumps from forming and ensures a silky sauce consistency.
Thicken Sauce: Reduce heat to low and let the mixture simmer, stirring occasionally, until it thickens. The sauce should coat the back of a spoon when properly thickened.
Add Spinach: Add fresh spinach to the sauce and cook for 1 minute, or until wilted. The spinach will significantly reduce in volume as it cooks.
Incorporate Ham and Cheese: Add diced ham and 1 cup of grated Swiss cheese into the sauce, stirring until well combined. Remove from heat and set aside. The residual heat will melt the cheese into the sauce.
Assemble Pastries: Arrange puff pastry squares evenly on the prepared baking sheet. Top with a heaping spoonful of the ham and cheese mixture, then sprinkle with the remaining grated cheese. Distribute filling evenly for consistent baking.
Form Pastry Shape: Fold the corners of each puff pastry square toward the center to form a smaller square. This creates an attractive presentation while keeping the filling contained.
Apply Egg Wash: Brush the tops and sides of the pastries with lightly beaten egg white. This will give the pastries a beautiful golden-brown sheen when baked.
Bake: Bake for 18-20 minutes, or until pastries are puffed and golden brown. The pastry should be crisp and flaky, with the filling hot throughout.