Preheat the oven to 350 degrees F. Grease a bundt pan with softened butter, working it into every divot, then dust with flour and tap out the excess.
In a large mixing bowl, beat 6 large eggs and 2 cups granulated sugar together for 1 to 2 minutes.
Add 1 cup buttermilk, 1 cup vegetable oil, 1/4 cup butter, melted, and 2 teaspoons vanilla extract, and mix well.
Slowly mix in 3 cups all-purpose flour, 2 teaspoons baking powder, 1 teaspoon ground cinnamon, and 1 teaspoon salt until just combined. (You can whisk these ingredients together in a separate bowl if it makes you feel better, but I find that step to be unnecessary in this cake.)
In a small bowl, whisk together 1 cup brown sugar, packed and 2 teaspoons ground cinnamon.
Pour half the batter into the prepared pan and spread it level.
Sprinkle the brown sugar mixture evenly over the batter.
Then add the remaining batter until the brown sugar layer is covered.
Bake at 350 degrees F for 50 minutes. Remove from the oven and cool in the pan for 10 to 15 minutes, then turn the cake out onto a wire rack and let it cool completely.
Beat 3 ounces cream cheese, softened until smooth and creamy.
Add 1 1/2 cups powdered sugar and 2 tablespoons milk and beat until pourable.
Drizzle the icing evenly over the completely cooled cake.