For applesauce, simmer diced apple, sugar, butter and ginger until tender, about 20 minutes. Remove ginger, purée and chill.
For cakes, preheat oven to 325 °F. Grease and sugar 6 1½ -cup brioche tins or 12 muffin cups. Beat butter, oil and sugar with electric beaters until smooth. Add eggs one at a time, mixing well after each addition. Beat in vanilla. In a separate bowl, sift flour, cocoa, baking soda, salt and cinnamon. Whisk buttermilk and applesauce together. Add flour to butter mixture, alternating with applesauce, mixing well after each addition. Stir in chocolate chunks. Spoon batter into prepared tins and bake for 18 to 20 minutes, until cakes spring back when pressed. Allow cakes to cool in the pan 15 minutes, then turn out onto a cooling rack to cool completely.
For glaze, heat cream to just below a simmer and pour over chopped chocolate. Let sit for one minute then stir to smooth out. Stir in butter to melt in and thicken glaze. Pour over top of cakes and let drip deliciously down the sides. Top each cake with 3 hazelnuts.
Serve cakes at room temperature and store in an airtight container.