Pancake Batter: In a large bowl, using a wire whisk, combine flour, sugar, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a separate bowl, or large glass measuring cup, whisk together buttermilk and melted butter. Add milk and eggs. Beat until well combined.
Create a small well in the center of the dry ingredients. Add the wet ingredients and pumpkin purée. Mix with a wire whisk until the batter is smooth. Set aside while you make the cinnamon filling.
Cinnamon Filling: In a small bowl, combine 6 tablespoons of melted butter, ¼ cup granulated sugar, 2 teaspoons of cinnamon and 1 tablespoon of pancake batter. Mix until smooth. Place the mixture in a sandwich-sized Ziploc bag. As it cools, you may need to give the bag a little knead. Snip off a small piece of the corner of the baggie.
Preheat the griddle to 325° degrees. Spray with non-stick cooking spray. Use a ladle to add the batter to the pan. Spread the batter into a nice even circle. Pick up your cinnamon-filled baggie. Starting in the center of the pancake, squeeze the cinnamon filling on top of the pancake batter in a swirled pattern.
Cook the pancakes 3 to 4 minutes, until a majority of the bubbles have burst, and it is golden brown on the bottom. Slide a thin spatula underneath the pancake and gently, but quickly, flip the pancake over.
Cook an additional 2–3 minutes, until the other side is golden as well. Flip the pancakes onto a plate. You will see the cinnamon swirl has created a crater of cinnamon. Wipe off your griddle or pan, carefully with a paper towel, and repeat with the remaining pancake batter. Serve pancakes with your favorite syrup.