Preheat the oven to 350°F (175°C). Grease a mini bundt cake pan with non-stick spray or butter.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the butter mixture, alternating with the buttermilk. Begin and end with the dry ingredients, mixing until just combined.
Fill each mini bundt cake cavity about 2/3 full with batter. Bake for 15-18 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
Once cooled, use a small knife to create a hole in the center of each cake and fill it with prepared vanilla pudding.
In a small saucepan, heat the heavy cream over medium heat until it begins to simmer. Remove from heat and add the chocolate chips, stirring until melted and smooth.
Drizzle the chocolate ganache over the filled mini bundt cakes. Let set for a few minutes before serving.