In a large bowl, whisk together the flour, cornmeal, baking powder, baking soda, cinnamon, and salt. Set aside.
In a medium bowl, whisk together the pumpkin puree, buttermilk, eggs, and honey. Set aside.
Add 6 tablespoons of butter to a light-colored or stainless steel skillet and melt over medium heat.
Cook the butter, stirring often. After a few minutes, the butter should start to bubble.
As the butter goes from bubbly to foamy, keep stirring for 2 to 3 more minutes. The butter should turn golden brown and brown specs will settle at the bottom of the pan. It should smell nutty. Be careful not to overcook the butter, as it can burn quickly.
Pour the butter into a heat-proof container and let it cool for 5 minutes.
Mix the brown butter into the wet ingredients.
Remove the hot skillet from the oven and add the remaining 2 tablespoons butter to it. Swirl until melted and sizzling.
Scoop the batter into the skillet and smooth the top with a spatula.
Sprinkle the flaky sea salt evenly over the batter.
Bake for 28 to 32 minutes, until the edges are deep golden and pulling away from the sides, the center springs back when pressed, and a toothpick comes out with just a few dry crumbs.
Remove the skillet from the oven and let rest for 15 minutes.
Slice the cornbread into 8 wedges and serve warm with more butter and honey.