Preheat the oven to 350°F (177°C) and grease a 10-inch bundt pan with butter.
Mix the flour, baking soda, salt and pumpkin spice in a large bowl.
In separate bowl, mix the pumpkin puree, brown sugar, mashed banana, oil, eggs, and vanilla extract until combined. Pour the mixture into the flour and whisk until a thick batter is formed.
Mix the cream cheese with egg and granulated sugar until well combined. Its ok if a few small lumps remain.
Spread half of the pumpkin batter into the bundt pan then spread all of the cream cheese filling on top. Spread the remaining pumpkin batter on top and bake for 1 hour or until a toothpick inserted into the cake comes out clean.
When cake is completely cooked Once done, remove from the oven and allow to cool for 1 hour in the pan. Then, invert the bundt cake onto a wire rack to cool for another hour.