How to Make It
In a medium skillet, melt 1 tablespoon of butter until foaming. Add the sage and cook over moderately high heat, stirring, until crisp, about 30 seconds. Transfer to a paper towel–lined plate. Melt another 1 tablespoon of the butter in the skillet until foaming. Add the shallot and cook over moderately high heat until translucent, about 1 minute. Add the pumpkin puree, salt, pepper and 1/2 cup of the heavy cream and stir until very thick and reduced to 1 cup, about 4 minutes. Scrape the pumpkin mixture into a bowl and stir in the remaining 1/2 cup of heavy cream and the milk. Let cool to room temperature, then refrigerate until chilled, about 1 hour.
Preheat the oven to 350° and line a baking sheet with parchment paper. In a medium bowl, whisk the 2 cups of flour with the baking powder. Using a pastry blender or 2 knives, cut in the 4 tablespoons of cubed butter until the mixture resembles coarse meal. Add the diced cheese and toss to coat. Add the sage and the pumpkin mixture and stir just until combined.
Melt the remaining 2 tablespoons of butter. Turn the dough out onto a lightly floured surface and pat it into a 6-by-9-inch rectangle, 1 inch thick. Cut into 6 large triangles and transfer to the prepared baking sheet. Brush the tops of the scones with the melted butter and sprinkle with the shredded cheese. Bake until golden and puffy, about 25 minutes. Transfer to a wire rack to cool slightly; serve warm.