Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a large mixing bowl, whisk together the gluten-free flour, brown sugar, baking powder, baking soda, and salt.
Add the cold, cubed butter to the flour mixture. Use a pastry cutter or your fingers to cut the butter into the flour until the mixture resembles coarse crumbs.
In a separate bowl, whisk together the butternut squash puree, egg, and vanilla extract.
Pour the wet ingredients into the dry ingredients and stir until just combined. Fold in the chopped pecans.
Turn the dough out onto a lightly floured surface and shape it into a disk about 1 inch thick. Cut the disk into 8 wedges and place them on the prepared baking sheet.
Bake for 20-25 minutes, or until the scones are golden brown and a toothpick inserted into the center comes out clean.
Allow the scones to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.