Thaw the pastry sheets at room temperature for 40 minutes or until they're easy to handle. Heat the oven to 400 degrees F. Stir the egg and water in a small bowl with a fork.
Pound the chicken to 1/4-inch thickness. Cut each chicken breast in half. Coat the chicken with the flour.
Heat the oil in a 12-inch skillet over medium-high heat. Add the chicken and cook until it's well browned on both sides. Remove the chicken to a plate. Cover the plate and refrigerate for 15 minutes.
Stir the spinach and nutmeg in the skillet. Reduce the heat to medium. Cook for 5 minutes or until the mixture is hot, stirring often.
Unfold 1 pastry sheet on a lightly floured surface. Roll the pastry sheet into a 14-inch square. Cut the pastry sheet into 4 (7-inch) squares. Repeat with the remaining pastry sheet. Brush the edges of the pastry squares with the egg mixture
Place 1 chicken piece in the center of each of 4 pastry squares. Spread each with 1 teaspoon mustard and top with about 1/4 cup spinach mixture. Top each with another pastry square. Press the edges to seal. Brush the pastries with the egg mixture. Place the pastries on a baking sheet.
Bake for 25 minutes or until the pastries are golden.