Preheat oven to 400 degrees.
Add the flour, brown sugar, pumpkin spice, baking powder, baking soda, and salt to a large mixing bowl and whisk to combine.
Add the cold butter to the bowl and use a pastry cutter to cut the mixture together until you have coarse crumbs.
In a small bowl, whisk together the pumpkin, milk, and egg. Stir into the dry ingredients until just moistened.
Turn dough out onto a floured surface and knead 5 times, just to bring the dough together.
Shape the dough into a circle and cut into 8 wedges.
Place the scones on an ungreased baking sheet and bake for 12 minutes or until golden brown. Let cool for 20 minutes.
To make the glaze, whisk together the powdered sugar and milk until well combined. Add more milk as needed to thin the glaze to your liking.
Spoon the glaze over the top of the scones, being sure to leave about ½ cup of glaze leftover.
Whisk the pumpkin pie spice into the remaining glaze. Add an additional tablespoon or two of powdered sugar for a thicker consistency, if desired.
Lightly drizzle the remaining glaze over the top of the scones.
Let glaze set before storing, tightly covered, at room temperature.