Preheat oven to 400 degrees. Line a large baking sheet or two small baking sheets with parchment paper or lightly grease with cooking spray.
To make the dough for the scones, whisk the flour, sugar, baking powder, salt, cinnamon, and pumpkin pie spice together.
Dice the butter into small cubes. Add to dry ingredients. Cut butter into the dry ingredients using a fork or a pastry cutter until mixture resembles coarse crumbs.
In a separate bowl, mix the pumpkin puree, milk, egg and vanilla. Stir into the flour and butter mixture until a soft dough forms. Work in the chocolate chips. Transfer the dough to a well-floured surface and knead for 20-30 seconds until it comes together.
Shape the dough into a 12-inch circle. Cut the the circle into 8 equal size triangles. Place on prepared baking sheet (not touching each other) and bake for 10-15 minutes until browned.
While scones are baking, prepare the frosting. Cream together butter, cream cheese, vanilla, and maple extract. Add powdered sugar and mix well. Add milk 1 tablespoon at a time until mixture is smooth and pourable. Spread or pour over cooled scones. Store in airtight container at room temperature.