Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, brown sugar, baking powder, cinnamon, nutmeg, ginger, and salt until combined.
Add the cubed butter into the dry mixture using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
In a separate bowl, whisk together the pumpkin puree, heavy cream, egg, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. If desired, fold in the chopped walnuts or pecans.
Transfer the dough onto a floured surface and gently knead it a few times until it comes together. Pat it into a round disc about 1-inch thick.
Cut the dough into 8 equal triangles (like a pizza) and place them onto the prepared baking sheet, spacing them slightly apart.
Bake in the preheated oven for 15-18 minutes, or until the scones are golden-brown and a toothpick comes out clean.
While the scones cool, prepare the icing by whisking together the powdered sugar and milk in a small bowl until smooth. Adjust the consistency with more milk if needed.
Drizzle or spread the icing over the scones once they are completely cool.