MAKE THE CAKE and MAKE THE GLAZE
MAKE THE CAKE
Preheat your oven to 400F.
Peel, core, and slice the apples.
Mix together the 1/2 cup sugar and 1 1/4 tablespoon of cinnamon. Toss the apples in the cinnamon sugar and place on a parchment lined sheet tray. Bake the apples for 8-10 minutes, until the sugar melts and bubbles around the slices and they are still slightly firm.
Turn the oven down to 325F.
Butter and flour a 9 1/4" Savarin mold or a 1-pound loaf pan.
In a medium bowl, mix and sift the chestnut flour, all-purpose flour, salt, baking powder, and sugar.
In a mixing bowl fitted with the whisk attachment, mix together the melted butter, milk, and egg.
Add the dry ingredients to the wet ingredients, stirring just until combined. Add the roasted apples to the batter and fill your desired pan.
Bake for 20-30 minutes. The Savarin pan will take less time to bake than the loaf pan because it allows for the oven to more evenly cook the batter. Test the cake by inserting a toothpick in the center. If it pulls out clean then the cake is done. If it comes out with sticky, wet crumbs then it still needs a few minutes.
Remove from oven and place on a cooling rack.
MAKE THE GLAZE
Mix the apple cider, cinnamon stick, and cloves in a medium saucepan and reduce the cider to 1 cup. Remove the cinnamon stick and cloves and whisk the powdered sugar into the hot cider.
Glaze the cake while both the cake and glaze are still warm.