Preheat the oven to 400°F. Spray a 9x9-inch baking pan with nonstick cooking spray.
In a medium bowl, whisk together the cornmeal, flour, baking powder, baking soda, salt, pumpkin pie spice, and cinnamon. Set aside.
In a large bowl, whisk together the eggs, sugar, pumpkin puree, and buttermilk until smooth.
Add the dry ingredients to the wet ingredients and stir gently just until combined. The batter will be slightly lumpy—avoid overmixing.
Pour the batter evenly into the prepared pan and spread to the edges.
Bake for 25–30 minutes, or until a toothpick inserted in the center comes out clean.
Remove from the oven and immediately spread the butter over the warm cornbread.
Cool in the pan on a wire rack for 10–15 minutes before cutting and serving.