Prep the pan and oven: Heat the oven to 350°F (175°C). Generously grease a 10–12 cup bundt pan with softened butter, then dust with flour and tap out the excess.
Make sure every ridge is coated to prevent sticking.
Mix the cinnamon swirl: In a small bowl, combine 1/2 cup light brown sugar, 2 teaspoons ground cinnamon, a pinch of salt, and 3 tablespoons melted butter. Stir until sandy and set aside.
Whisk the dry ingredients: In a large bowl, whisk 2 3/4 cups all-purpose flour, 1 1/2 cups granulated sugar, 2 teaspoons baking powder, 1/2 teaspoon baking soda, and 3/4 teaspoon fine salt.
Combine the wet ingredients: In a separate bowl, whisk 3 large eggs, 3/4 cup sour cream, 3/4 cup whole milk, 1/2 cup neutral oil, and 2 teaspoons vanilla extract until smooth and glossy.
Make the batter: Pour the wet mixture into the dry. Stir with a spatula just until combined and no dry pockets remain.
The batter should be thick but pourable; don’t overmix.
Layer and swirl: Spoon half the batter into the prepared pan and smooth it evenly. Sprinkle the cinnamon mixture over the batter in an even ring. Top with the remaining batter, smoothing to the edges.
Use a butter knife to gently swirl once or twice—less is more to keep defined ribbons.
Bake: Place the pan on the center rack and bake for 45–55 minutes, or until a toothpick inserted near the center comes out clean or with a few moist crumbs. The top should spring back lightly to the touch.
Cool properly: Let the cake cool in the pan for 12–15 minutes. Run a thin offset spatula around the edges and inner tube, then invert onto a wire rack.
Cool completely before drizzling.
Make the cream cheese drizzle: Beat 4 ounces softened cream cheese with 1 cup powdered sugar until smooth. Add 1–3 tablespoons heavy cream (or milk), a pinch of salt, and 1/2 teaspoon vanilla. Blend until thick but pourable.
Adjust with more cream to reach a slow-drip consistency.
Finish and serve: Spoon or pipe the drizzle over the cooled cake, letting it cascade down the ridges. For extra flair, dust with a tiny pinch of cinnamon or top with chopped toasted pecans. Slice and enjoy.