In medium bowl, using a hand mixer or whisk, stir the pumpkin, cream cheese, sugar, and pumpkin pie spice until well blended.
Spoon a rounded teaspoonful of the mixture into each dough-filled muffin cup, and spread slightly.
Bake 8 to 12 minutes or until edges are light golden brown and filling appears set (cookies and filling will be soft). Cool 10 minutes in pan. Be sure to leave them in the pan the 10 minutes, this will make it easier to remove the cookies from the pan. I found that using an offset spatula around the sides of each cookie to loosen them worked well. Then carefully remove to cooling rack to cool completely.
To easily top the cookies with frosting: Fill small resealable food-storage plastic bag with frosting. Cut off small corner of bag; squeeze small dollop of frosting onto each cookie.
Sprinkle lightly with pumpkin pie spice, if desired. Refrigerate cookies in covered container or resealable food-storage plastic bag.