Prepare a large baking sheet with parchment paper and set aside.
To brown the butter, melt 2 sticks of butter in a large skillet and heat on medium to medium-low heat, stirring frequently. Heat until the butter starts to bubble and the solids start to turn a dark brown color. The butter will give off a rich, nutty scent.
Transfer the butter to a bowl and let it chill in the fridge until solid, mixing occasionally to make sure the solids incorporate back into the butter.
When butter is solid, whisk together the flour, sugars, baking powder, salt, and pumpkin pie spice in a large bowl.
Measure out 113g of solid brown butter and add it to the dry ingredients. Save the remaining butter for the icing.
With a pastry cutter or fork, cut in the butter until almost fully incorporated into the dry ingredients.
In a separate bowl, whisk together the milk, egg, pumpkin puree, and vanilla extract.
Pour the wet ingredients over the dry, mixing until roughly combined into a shaggy dough, then move the dough to a floured surface and gently knead for a few minutes into a rough ball.
Form the dough into a flattened circle and cut 6-8 wedges, placing them slightly apart on your prepared baking sheet.
Chill scones in the fridge while you preheat your oven to 400ºF.
Brush the tops of the scones lightly with milk and sprinkle with brown sugar if desired.
Bake for 20 minutes or until golden brown and risen slightly.