Preheat oven to 350 degrees F. Line a cookie sheet with parchment paper, set aside. In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add brown sugar, pumpkin pie spice, and salt. Beat until combined, scraping side of bowl occasionally. Gradually beat in as much of the four as you can with the mixer (I got all of it mixed in). Using a wooden spoon, stir in any remaining flour.
Shape dough into 1-inch balls. Place balls 2 inches apart on prepared cookie sheet. Coat the bottom of a cookie stamp with nonstick cooking spray and dip the stamp in granulated sugar and cinnamon mixture. Flatten each ball of dough, imprinting the press pattern on the cookie.
Bake in preheated oven for 12 to 15 (mine took 16) minutes or until lightly browned. Transfer cookies to a wire rack; let cool. Makes about 36 cookies.
To Store: Layer cookies between waxed paper in an airtight container, cover. Store at room temperature for up to 3 days or freeze for up to 3 months.