Preheat the oven to 375 degrees.  Strain the pumpkin puree and squeeze out any extra liquid. Mix the butter, sugars, egg, and pumpkin together in a mixer until blended.  Add the espresso and vanilla extract and mix to incorporate.  In another bowl mix the baking soda, baking powder, cinnamon, and salt. Slowly add the flour one cup at a time until the flour is mixed in completely. Mix the wet ingredients into the dry until thoroughly blended.

Put the dough in the refrigerator for 15 minutes. Grease the scone pan and set it aside.  Scoop the dough into each section of the scone pan, and be sure to smooth the top of the scone mixture so it is flat in the pan. If you do not have a scone pan, drop large rounded spoonfuls of scone dough onto a lined baking sheet and flatten with the top of the spoon. Bake in the oven for about 20-25 minutes until golden. Use a toothpick in the center of a scone to make certain it is baked thoroughly. Cool the scones for about 15 minutes before adding the glaze. Whisk the powdered sugar, milk, and brewed espresso together and drizzle over the scones.

Note: These scones have a more cake-like texture than traditional scones.