Step 1: Prepare Brown Butter - Melt two sticks of unsalted butter in a medium saucepan over medium heat, stirring continuously for 5-7 minutes until deep golden brown and nutty aroma is emitted. Remove from heat and let cool until solid.

Step 2: Mix Dry Ingredients - In a large mixing bowl, whisk together flour, granulated sugar, light brown sugar, baking powder, salt, and pumpkin pie spice until well combined.

Step 3: Combine Mixtures - Cut solidified brown butter into small pieces and mix into dry ingredients. In a separate bowl, whisk together milk, egg, pumpkin puree, and vanilla extract. Pour wet mixture into dry ingredients and gently mix until a shaggy dough forms.

Step 4: Shape Scones - Turn dough onto a floured surface and gently knead. Flatten into a 1-inch thick circle. Slice into wedges and transfer to a parchment-lined baking sheet.

Step 5: Chill and Bake - Refrigerate shaped scones for 20 minutes while preheating the oven to 400ºF (200ºC). Brush tops with milk and sprinkle with brown sugar. Bake for 20 minutes or until golden brown.

Step 6: Prepare Icing - Melt remaining brown butter in a small saucepan. Combine with powdered sugar and vanilla in a bowl, whisking until smooth. Adjust consistency with milk if necessary.

Step 7: Serve - Drizzle the icing over warm scones and let set before serving, best enjoyed with coffee or tea.