Brown Butter, Apple, and Hazelnut Tea Cakes (GF)

Today I decided to make something alarmingly unseasonal. I was mildly horrified at my own audacity, but the final product reassured me that I had picked the right recipe. I initially chose the recipe - Cannelle et Vanille's recipe for brown butter, hazelnut, and pear cakes - because our only remaining fruit was a lone apple, and I planned to substitute said apple for the two pears that the recipe called for. The fates must have been with me, however, for just as I was setting out my ingredients, my sister and father returned from the grocery store with a whole bag of apples. Some might call this a happy coincidence...I prefer to call it destiny. 
These little cakes worked out beautifully. Soft and moist from the apples, one would never guess that they are gluten-free. The hazelnuts add a pleasant nutty flavor, and the cinnamon sugar coating makes them almost doughnut-like. I have decided that these cakes, although they seem distinctly autumnal, are good enough to be made in any season. 

Brown Butter, Apple, and Hazelnut Tea Cakes (GF)
Adapted from Cannelle et Vanille

   1 cup (125 g) brown rice flour
   1/2 cup (50 g) hazelnut flour (or hazelnuts ground as fine as possible in the food processor)
   2 tbsp (20 g) tapioca starch
   1/8 tsp xanthan gum
   1 1/2 tsp baking powder
   1/4 tsp salt
   1/2 tsp cinnamon
   10 tbsp butter, browned
   1/3 cup (85 g) brown sugar
   1/3 cup (100 g) maple syrup
   1 tsp vanilla extract
   2 eggs
   3 apples - 2 grated, 1 thinly sliced crosswise in rings (preferably with a mandoline)
   1 tbsp butter, melted
   1/2 cup sugar
   1/2 tsp cinnamon
   3 tbsp ground hazelnuts (for garnish - optional)

Preheat the oven to 350˚F and grease a muffin tin.
In a small saucepan, cook the butter over medium heat until it starts to brown and develops a nutty smell. Strain the brown butter and set aside to cool slightly. Either use a metal sieve, or let it cool in the pan before using a plastic one as I ruined a plastic sieve by pouring the hot butter through it. 
In a separate bowl, whisk together the flours, tapioca starch, xanthan gum, baking powder, salt, and cinnamon. 
In another medium bowl or in the bowl of a stand mixer, whisk together the eggs, brown sugar, maple syrup, and vanilla extract for about 5 minutes until the mixture is light and thick. Add the cooled brown butter and whisk until incorporated.
Add the dry ingredients to the wet ones and combine. Fold in the grated apples. I used about 3/4 of the two apples I had grated, but it will depend on the size of your apples. Mine were fairly large.  
Before dividing the batter, use a cookie cutter to slice your apple slices into small circles just about the size of the bottom of the wells of your muffin tin. Dip each slice in the melted butter before placing one in each of the wells of the pan, butter side down.
Divide the batter among the twelve wells of the muffin tin and bake for 20-22 minutes. They should be golden brown and a toothpick should come out clean when inserted into the center of one of the cakes. Allow them to cool for five minutes before running a butter knife around the edge of each muffin and carefully removing from the tin. 
Mix the sugar and cinnamon. Dip the top and roll the sides of each cake in the cinnamon sugar mixture. Sprinkle each one with some ground hazelnuts.