Preheat the oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.

Sift flour, baking powder, baking soda, salt, and pumpkin pie spice for cookies together in a large bowl. Set aside.

Combine shortening and brown sugar in a second large bowl. Beat using an electric mixer until light and fluffy, about 1 minute. Add pumpkin, egg, and vanilla extract; mix well until combined. Add 1/2 of the flour mixture and mix well. Add remaining flour mixture and mix again.

Scoop tablespoonfuls of dough onto the prepared baking sheets, arranging 2 inches apart.

Bake in the preheated oven until lightly browned at the edges, about 14 minutes, rotating baking sheets from top to bottom and front to back halfway through baking time.

While the cookies bake, combine butter and maple syrup for icing in a medium bowl. Beat using an electric mixer until smooth. Add pumpkin, pumpkin pie spice, and vanilla extract. Mix well. Add powdered sugar and beat until fluffy. Add food coloring and beat until uniform. Set aside.

Remove cookies from the oven and let cool on baking sheets for 5 minutes. Transfer cookies to a wire rack to cool completely, 20 to 30 minutes more. Pipe or spread icing onto cooled cookies and decorate with sprinkles as desired.