Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
Beat butter and sugar until light and fluffy.
Add maple syrup and eggs, one at a time.
Then mix in the pumpkin.
Whisk flour, baking powder, cinnamon, allspice, nutmeg, and cloves separately.
Gradually add to the pumpkin mixture and mix until combined.
Fold in the chocolate chips.
Scoop dough onto the prepared baking sheets, leaving about 2 inches between cookies.
Bake for 12 minutes, until the centers are set.
Cool on the baking sheet for a few minutes, then transfer to a wire rack and cool completely.
For the frosting, beat cream cheese until smooth and fluffy.
Gradually mix in powdered sugar.
Then add milk and vanilla.
Fold in lemon zest. If the frosting is too thin, add another ¼ cup powdered sugar
Frost the cooled cookies before serving.