Preheat oven to 350 F degrees and grease a bundt pan with butter or cooking spray.
Start by making the cream cheese filling. Add all the cream cheese filling ingredients the bowl of your mixer and mix until well incorporated, about 2 minutes. Set this mixture aside. Clean the mixer bowl.
Add the butter and brown sugar to the bowl of your mixer and mix for 2 minutes on medium high. Add the eggs and continue mixing for another 2 or 3 minutes until mixture lightens up.
While that's mixing, add the flour, baking powder, baking soda, salt and pumpkin pie spice to a bowl and stir it all together. Set aside.
Add the buttermilk and pumpkin puree to the mixer and mix until well incorporated, another minute.
Add the flour mixture to the mixer and mix for one more minute until all the flour has been incorporated into the mixture.
Pour half of the batter into the prepared bundt pan and spread evenly all around. Pour the cream cheese mixture over the pumpkin cake batter and spread this around the bundt pan. Pour the remaining cake batter over the cream cheese filling and spread as evenly as you can.
Bake for about 55 minutes or until cake is done. Insert a toothpick into the center of the cake and if it comes out clean, the cake is done.
While the cake is baking, make the cream cheese icing. Add all the ingredients for the icing to the bowl of your mixer and mix for about 3 minutes or until smooth. Add more milk as necessary, for a thicker icing use less milk, for an icing that is easier to drizzle, add a bit more milk.
Take the cake out of the oven and let it sit in the bundt pan for about 5 minutes. Run a knife along the sides of the cake if necessary, then flip the cake over onto a cake tray. Let the cake cool a bit for about 10 to 20 minutes.
Drizzle with the cream cheese icing and top with chopped pecans if preferred.