Preheat oven to 350 degrees F. Line baking sheets with parchment paper. In a large bowl, combine flour, baking powder, baking soda, cinnamon, nutmeg, ground cloves, and salt; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and sugars. Add pumpkin, egg, and vanilla to butter mixture, and beat until creamy. Stir in the dry ingredients into the pumpkin mixture by hand until just combined. Drop on prepared baking sheets by heaping tablespoonfuls; Butter the bottom of a drinking glass and then dip the bottom of the glass in a bowl of sugar. Flatten the dough balls with the bottom of the glass until they are about ¾ inch thick, dipping the glass in sugar as necessary to prevent sticking.
Bake in preheated oven for 13 to 15 minutes. Cool cookies on wire rack. Once cookies have cooled completely, frost or drizzle with cream cheese frosting.
While the cookies are cooling make frosting: In the bowl of a stand mixer fitted with the paddle attachment, combine cream cheese, confectioners’ sugar and pumpkin pie spice and beat until smooth and creamy.