Preheat oven to 350F. Grease a 24-count mini muffin pan (preferred) or a 12-count standard size muffin pan with cooking spray.
In a medium bowl, mix together the gluten-free flour, almond flour, baking powder, baking soda, salt and nutmeg. In the bowl of a stand mixer, combine the eggs and granulated sugar. Mix on medium speedy until light and foamy, about 2 minutes.
With the mixer running on low, slowly pour in the vegetable oil and vanilla extract. Slowly pour in the flour mixture and mix to combine, followed by the buttermilk (or almond milk/cider vinegar mixture). Mix to fully combine, scraping down the bottom/sides of the bowl in between mixing.
Scoop the batter into the prepared muffin pan, filling only ⅔ of the way.
Bake mini puffs for 15-17 minutes, or standard-sized puffs for 22-25 minutes. When finished, the puffs will feel springy to the touch and a toothpick inserted into the center will come out clean. Let cool for 2-3 minutes in the pan, then transfer to a wire cooling rack.
After the puffs cool for 5-10 minutes, roll them in the brown butter (or dip the top) followed by the cinnamon sugar. Serve immediately. These are best hot, right out of the oven. Enjoy!