For the Cookies, mix flour, pumpkin pie spice and salt in medium bowl. Set aside. Beat butter and sugar in large bowl with electric mixer on medium speed until light and fluffy. Gradually beat in flour mixture on low speed until well mixed. Add water and vanilla; mix well. Press dough into a thick flat disk. Wrap in plastic wrap. Refrigerate 1 hour.
For the Filling, mix all ingredients in medium bowl until well blended. Refrigerate until ready to use.
Preheat oven to 350°F. Roll out dough to 1/8-inch thickness on lightly floured work surface. Cut out with 3-inch round or pumpkin-shaped cookie cutter. Set aside 1/2 of the dough rounds for the bottoms of the cookies. Score the top of remaining cookies with a small knife to make a pumpkin design or other desired designs.
To assemble the cookies, place about 2 teaspoon filling on each of the cookie bottoms. Moisten edges of cookies. Top each with a cookie top. Press edges with tines of a fork to seal the cookie. Brush top of each cookie with beaten egg. Place 2 inches apart on parchment paper-lined baking sheet.
Bake 20 to 22 minutes or until lightly browned. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.