Heat the oven: Heat the oven to 375°F. Grease a 10-inch cast-iron skillet generously with butter and set it aside.
Whisk the dry ingredients: Whisk the cornmeal, flour, baking powder, baking soda, salt, cinnamon, pumpkin pie spice, and sugar in a large bowl until evenly mixed.
Whisk the wet ingredients: Whisk the pumpkin puree, eggs, buttermilk, melted butter, and vanilla in a second bowl until smooth.
Combine gently: Pour the wet mixture into the dry mixture and stir with a spatula just until no dry streaks remain. Do not overmix, or the crumb turns tough.
Bake: Scrape the batter into the prepared skillet and smooth the top. Bake for 25 to 30 minutes, until golden and a toothpick inserted in the center comes out with a few moist crumbs.
Cool and slice: Cool in the skillet for 10 minutes, then slice into 8 wedges and serve warm.