Preheat oven to 350-degrees F. Line a cookie sheet or pan (18- x 13-inches) with a Silpat mat; set aside. Note: Pans may be buttered lightly instead of using a Silpat.
In a medium mixing bowl, whisk together flour, baking powder, baking soda, pumpkin pie spice and salt until well mixed. Set aside.
In a large mixing bowl, beat together butter and brown sugar until well blended. Add the pumpkin, egg and vanilla and mix well.
Add the flour mixture to the wet ingredients, a little at a time, stirring together lightly by hand after each addition. After the last addition of flour, mix only until ingredients are well combined. By hand, stir in the butterscotch chips.
Using a #24 scoop (3 tablespoons), place 8 scoops of cookie dough, evenly staggered, per baking sheet. The cookies need generous space between them to allow for spread and even cooking. Bake for 14-17 minutes, just until set. They should resist when lightly touched. (See #5 in "Notes")
Remove cookies from oven and allow to stand on pan for about 2 minutes. Remove cookies from pan and allow to cool completely on a wire rack. Store in an airtight container with either parchment paper of wax paper between layers.