Preheat oven to 375 degrees.
Whisk together flour, baking soda, baking powder, pumpkin-pie spice, and salt; set aside.
In a separate bowl, beat together butter and sugar with an electric mixer, until light and fluffy.
Add egg; beat until smooth.
With mixer on low speed, alternately add flour mixture and pumpkin puree a little at a time. Mix just until combined (do not over mix).
Drop dough by heaping tablespoons onto two baking sheets, about 1 1/2 inches apart.
Bake for 8 minutes, then rotate the cookies in the oven to bake evenly.
Bake an additional 8 - 12 minutes or until edges are golden and cookies puff up.
Immediately transfer cookies to wire racks, and cool completely.
When cookies have cooled, set them (still on rack) over a baking sheet or waxed paper.
Melt the chocolate by placing it in a glass bowl over (not in) a saucepan of simmering water, stirring to make sure it is melting evenly.
Remove from heat and pour chocolate into a plastic bag. Snip off a corner and pipe chocolate over cookies.
Refrigerate for about 20 minutes or until chocolate is firm.