Preheat the oven to 350 degrees. 

Spray a Bundt cake pan with nonstick spray and then a light coat of flour. Shake out any excess flour.

In the bowl of a stand mixer (or a large mixing bowl), combine the pumpkin, brown sugar, sugar, eggs, oil, and vanilla and mix well.

Next, add in the flour, pumpkin pie spice, and baking powder and mix on low speed for one minute. Stop the machine, scrape down the sides, and mix again on medium speed for another minute.  

Pour about half of the cake batter into your prepared Bundt pan.

To make the filling: Combine the cream cheese, egg, and sugar in another bowl and mix well. Pour this mixture over the first layer of pumpkin batter in your Bundt pan.  

Pour the remaining pumpkin mixture over the cream cheese filling and spread to cover. 

Bake in the preheated oven for approximately 60 minutes or until slightly golden brown and a toothpick comes out clean.  

Allow to cool for at least an hour on a wire rack before attempting to invert and remove from the pan.

When you're ready to glaze the cake, combine the powdered sugar, softened cream cheese, and milk in a bowl and mix well.

Carefully cover the bundt with a plate or serving platter and invert. It should release from the pan if completely cool. 

Drizzle the glaze over the cake.

When ready to serve, use a serrated knife to slice into pieces.