Position an oven rack in the middle of the oven and preheat the oven to 350℉. Grease and flour a 10-cup Bundt pan.
In a medium bowl, whisk together the 2 ½ cups gluten free flour, 1 cup almond flour, 2 teaspoons baking powder, ¼ teaspoon baking soda, 1 teaspoon fine sea salt, ¾ teaspoon ground nutmeg, ½ teaspoon ground ginger, and ½ teaspoon ground cardamom.
In a small bowl, mix together the 1 cup unsweetened pumpkin puree and ¾ cup buttermilk.
In a large bowl (or the bowl of a stand mixer), use an electric mixer to cream the 12 tablespoons unsalted butter on medium speed, about 1 minute. Add the ¾ cup brown sugar and ½ cup granulated sugar and beat until light and fluffy, 4 to 6 minutes. Add the 3 large eggs one at a time, beating until incorporated and scraping down the bowl as needed.
On low speed, mix in one-third of the flour mixture, then add the pumpkin-buttermilk mixture, and finish with the remaining flour mixture. Scrape down the bowl with a rubber spatula and mix the batter a few times, then pour the batter into the prepared pan and smooth the top. Rest the batter for 15 minutes, then place in the oven and bake the cake until a tester inserted near the center comes out clean, 55-65 minutes.
Transfer the pan to a wire rack and let cool for 15 minutes, then flip it out of the pan onto the rack to cool completely.
Make topping: In a small bowl, mix together the granulated sugar and cinnamon. Brush the tops and the sides of the cake with the melted butter, then sprinkle with the cinnamon sugar, using your hands to gently rub it into the sides. Cool to room temperature before serving.
Make sure the ingredients are at room temperature. This is a cake that needs butter that's first been brought to room temperature so that it seamlessly blends with the sugar. If you don't have time to let the butter soften, place it in the microwave for about 10 seconds to soften it up a bit.
Prep that bundt pan! I don't even want to tell you about my novice bundt-baking failures! Suffice to say, they didn't result in a pretty cake. But it's totally avoidable. My best advice for baking bundt cakes is to use a lot of softened butter to get into every nook and cranny of the pan, and use a liberal hand. You can also dust the pan with gluten-free flour, but I find that when I grease it very well, this does the trick.
Try pumpkin pie spice. For a slightly different flavor, swap the cinnamon in the topping for pumpkin pie spice.
Dairy-free. Make this cake dairy-free by using dairy-free butter and dairy-free milk or yogurt for the buttermilk.
Buttermilk substitute. I prefer real buttermilk here because it brings a tenderness to the cake you don't get from milk. However, if you're out, my first choice for a substitute is an equal mix of plain yogurt and milk. In a real pinch, add 1 tablespoon of vinegar to 1 cup of milk, let it stand for 10 minutes, then measure out what you need in place of the buttermilk.