Prepare the Cake Layers:

1. Preheat the oven to 350°F (175°C). Grease and flour two 8-inch round cake pans.
2. In a large bowl, whisk together the flour, sugar, cocoa powder, baking powder, baking soda, and salt.
3. In another bowl, mix the oil, eggs, buttermilk, vanilla extract, and mint extract.
4. Gradually add the wet ingredients to the dry ingredients, stirring until just combined.
5. Divide the batter evenly between the prepared pans and bake for 25-30 minutes, until a toothpick inserted into the center comes out clean. Let the cakes cool completely.

2. Prepare the Cheesecake Layer:

1. Reduce the oven temperature to 325°F (163°C).
2. In a mixing bowl, beat the cream cheese and sugar until smooth. Add the egg, sour cream, vanilla extract, and mint extract, mixing until well combined.
3. Pour the cheesecake mixture into a greased 8-inch round pan and bake for 30-35 minutes, until the center is set. Allow it to cool completely.

3. Make the Mint Chocolate Ganache:

1. Heat the heavy cream in a small saucepan until it just begins to boil.
2. Pour the hot cream over the chocolate chips in a heatproof bowl. Let it sit for 2 minutes, then stir until smooth. Mix in the mint extract.

4. Assemble the Cake:

1. Place one cake layer on a serving plate and spread a layer of ganache on top.
2. Carefully place the cooled cheesecake layer over the ganache, then top with the second cake layer.
3. Pour the remaining ganache over the top of the cake, allowing it to drip down the sides.
4. Refrigerate the cake for at least 1 hour before serving to set the ganache.