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Heat the three tablespoons of brown sugar in a skillet. Add the chestnuts and toss and cook to caramelize. Remove from heat and let cool
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Peel and core the apple. cut the flesh into small pieces.
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Toss the apple pieces with the caramelized chestnuts.
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Preheat the oven to 350 degrees f.
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Grease and flour a bundt pan.
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In a separate bowl whisk together the flour, salt, and baking powder.
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Cream together the cup of brown sugar and the butter. Beat for 3 minutes.
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Add the eggs one at a time making sure each is incorporated fully into the batter before adding the next.
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Beat in the vanilla extract.
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Add the dry ingredients to the butter and beat until just combined.
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Mix in the caramelized chestnuts and apple pieces.
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Transfer the batter to the prepared bundt pan.
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Place the pan in the oven and bake for 45 minutes or until a knife inserted into the cake comes out clean.
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Remove from oven. Let the bundt cool in the pan for 15 minutes.
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Remove the cake from the pan and transfer it to a wire rack fitted over a baking sheet lined with baking paper.
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Let the cake cool completely.
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Add the apple brandy to the powdered sugar one tablespoon at a time, whisking to combine. Stop adding the brandy when the mixture reaches a pourable glaze.
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Drizzle the glaze over the cake.
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Let the glaze harden completely before slicing and serving.