Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone mats for easy baking.
In a large bowl, mix together pumpkin puree, maple syrup, brown sugar, and egg until well blended. Add vanilla extract and mix until combined.
In another bowl, whisk together flour, baking soda, pumpkin pie spice, and salt until thoroughly combined.
Gradually add the dry ingredients to the wet mixture. Stir just until combined, being careful not to overmix. The dough will be thick and sticky.
Using a cookie scoop or two tablespoons, drop rounded balls of dough onto the prepared baking sheets, about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden and the centers seem slightly soft. Remove them and let them cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.
Once cooled, enjoy your chewy maple pumpkin cookies with a glass of milk or your favorite warm beverage!