Preheat the oven to 350°F. Butter a 10-inch Bundt pan.
In a large bowl, whisk together all the cake ingredients, except the cream cheese. Mix until just combined. The batter will be thick.
In a separate bowl, whisk the softened cream cheese until creamy.
Spoon half the pumpkin batter into the prepared pan. Dollop the cream cheese over the batter. Spoon the remaining pumpkin batter over. Using a knife, gently swirl the layers together.
Bake for 55–65 minutes, until a toothpick inserted into the cake comes out clean. I bake mine for 55 minutes, tenting the cake with foil after 30 minutes.
Cool in the pan for 1-2 hours. Invert onto a serving plate.
To make the icing, add the butter to a pan over medium heat. Cook until lightly browned, 3 minutes. Remove from the heat. Whisk in the powdered sugar, milk, and cinnamon. Add additional milk as needed to thin.
Quickly pour the icing over the cake, allowing it to drip down the sides.