Heat the oven to 400°F. Line a baking sheet with parchment paper or lightly oil it. In a large bowl, combine the flours, sugar, dried thyme, baking powder, baking soda and salt. Grate the butter into the flour, tossing to coat. Add 1/2 cup of the Parmesan and toss to mix.
In a medium bowl, whisk together the pumpkin and cream. Stir into the dry mixture just until mixed, then add walnuts. Spread a little flour on the counter, then scrape the dough out onto the flour. Form into a round, and flatten to about an inch thick. Sprinkle with chopped thyme, top with remaining Parmesan, and pat down with your palms. Using a knife, divide the round into 8 wedges. Transfer to the baking sheet, leaving a couple of inches between the scones.
Bake for about 18–20 minutes, until the scones are golden around the edges and firm to the touch. Cool on racks before storing in a tightly covered container or bag.