1. Preheat oven to 350 degrees F. Line a large baking sheet with parchment paper or a silicone baking mat. Set aside.
2. In a medium bowl, whisk together the flour, baking soda, pumpkin pie spice, and salt. Set aside.
3. In the bowl of a stand mixer, beat butter, brown sugar and granulated sugar until light and fluffy. Add egg and vanilla extract. Beat until combined. Beat in the pumpkin and maple syrup until smooth. Gradually add flour mixture and mix until ingredients are incorporated. Stir in the oats.
4. Drop cookie dough by rounded tablespoons onto prepared baking sheet. Bake cookies for 12 minutes or until cookies are lightly browned. Cool on baking sheets for 2 minutes; transfer to wire racks to cool completely.
5. While the cookies are cooling, make the glaze. In a medium bowl, whisk together melted butter, powdered sugar, maple syrup, maple extract, vanilla extract, and milk. You may need to add a little more milk if the glaze is too thick. Whisk until smooth.
6. Drizzle maple glaze over cooled cookies. Let sit until glaze hardens. Serve and enjoy!