Preheat the oven to 350 degrees. Prepare the bundt pan by spraying it with non-stick spray and then dusting it with a light layer of flour. Tap out the excess flour and set it aside.
In the bowl of a stand mixer, combine the butter and sugar. Cream until smooth.
Add in the cocoa powder, baking powder, and salt. Mix until smooth.
Add in the eggs, milk, vanilla, and oil. Combine well, stopping the mixer, scraping the sides, and mixing again.
Finally, add in all of the flour and mix thoroughly. Pour about half of the chocolate batter into your prepared pan, reserving the rest for later. Set aside.
To make the filling, in the bowl of a stand mixer, combine the softened cream cheese, egg, and powdered sugar. Cream until smooth. Pour this mixture over the chocolate batter in the pan and spread evenly.
Top with the remaining chocolate batter and spread it evenly.
Place the bundt pan on a larger baking sheet to catch any drips. Bake in the preheated oven for 50-60 minutes or until a toothpick inserted into the cake comes out clean.
Allow the cake to cool completely before trying to remove it from the pan. When ready, invert the cake onto a plate or serving platter. If needed, use a butter knife to gently loosen the cake from the sides of the pan to release it.
When ready to serve, make the glaze. In the bowl of a stand mixer, combine the powdered sugar, softened cream cheese, and milk. Blend until smooth. Drizzle the glaze over the bundt cake and slice.