Preheat your oven to 325°F (163°C). Generously grease and flour a 10 to 12 cup Bundt pan.
In a medium bowl, stir together the ⅓ cup melted butter, ¾ cup brown sugar, 1 tablespoon flour, 1½ tablespoons cinnamon, pinch of salt, and 1 teaspoon vanilla extract until combined. Set aside.
In a large bowl, beat the 1½ cups unsalted butter, 8 ounces cream cheese, and 2½ cups granulated sugar together for about 5 minutes until very light and fluffy.
Add the 6 eggs one at a time, beating well after each addition. Mix in the 1 tablespoon vanilla extract and ½ teaspoon cinnamon.
In a separate bowl, whisk together the 3 cups cake flour, 1 teaspoon salt, and ¼ teaspoon baking soda.
Add the dry ingredients to the batter alternating with the 1 cup sour cream, beginning and ending with the flour mixture. Mix just until combined.
Spoon about one third of the batter into the prepared Bundt pan. Drizzle about one third of the cinnamon swirl mixture over the batter. Repeat the layers two more times, finishing with the swirl. Use a butter knife to gently swirl through the batter once or twice. Do not go wild here or you’ll lose the ribbon effect completely.
Bake for 1 hour 10 minutes to 1 hour 20 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool the cake in the pan for 15 minutes before carefully inverting onto a wire rack to cool completely.
For the icing, beat the 4 ounces cream cheese and 2 tablespoons butter together until smooth. Add the 1½ cups powdered sugar, 2 tablespoons milk, 1 teaspoon vanilla extract, and pinch of salt. Beat until creamy and pourable. Add another tablespoon of milk if needed.
Drizzle the icing over the cooled cake and sprinkle with a bit of cinnamon. Let it set slightly before slicing.