Preheat oven to 400 with a cast iron skillet in the oven.
In a large bowl stir together the cornmeal, flour, baking powder, baking soda, salt, brown sugar and pumpkin pie spice.
In a small bowl stir together the pumpkin puree, heavy cream, beer, olive oil, and eggs.
Make a well in the dry ingredients, pour in the wet ingredients and stir until just combined.
Carefully remove the hot pan from the oven, add the butter. Swirl around the pan until the butter is melted and the pan is well coated. Pour the excess butter into a small bowl.
Pour the batter into the pan in an even layer, pour the excess melted butter on the top.
Bake until the top springs back when lightly touched, 16-18 minutes.
Remove from oven, slice, serve warm.