Step 1

Place 3 sticks unsalted butter in a stand mixer. Place 6 large eggs and 1 cup sour cream on the counter. Let everything sit at room temperature until the butter is softened, about 1 hour. Sift enough cake flour to have 3 cups sifted flour.

Step 2

Arrange a rack in the middle of the oven and heat the oven to 325°F. Melt the remaining 1 tablespoon unsalted butter in a small bowl, add the remaining 1 tablespoon cake flour, and stir to make a paste. Brush the paste in a 12-cup Bundt pan, making sure to coat all the crevices and tube.

Step 3

Beat the butter with the whisk attachment on high speed until fluffy and slightly lighter in color, about 1 minute. With the mixer on low speed, slowly add 2 1/2 cups granulated sugar. Beat on medium speed until very pale yellow and fluffy, about 5 minutes. Beat in the eggs 1 at a time, beating well after each addition and scraping down the sides and bottom of the bowl as needed.

Step 4

With the mixer on at the lowest speed, slowly add the flour in 2 batches. Beat in 1 teaspoon kosher salt and 1/2 teaspoon baking soda. Be careful not to overbeat. Add the sour cream, 2 tablespoons vegetable oil, and 1 tablespoon vanilla extract. Scrape down the sides and bottom of the bowl and beat the batter until just combined. Be careful not to overmix.

Step 5

Place 5 tablespoons plus 1 teaspoon unsalted butter in a small microwave-safe bowl and microwave until melted (1/3 cup melted). (Alternatively, melt on the stovetop and transfer to a small bowl.)

Step 6

Add 1/3 cup packed brown sugar, 1 tablespoon cake flour, 1 1/2 teaspoons ground cinnamon, and 1 teaspoon vanilla extract, and whisk to combine. The mixture will be very runny.

Step 7

Pour 1/3 of the batter into the prepared pan. Drizzle 1/2 of the cinnamon swirl over the batter. Using a butter knife or skewer, swivel the mixture through the cake batter, creating a flourish pattern.

Step 8

Pour 1/2 of the remaining batter into the pan, drizzle with the remaining cinnamon swirl, and swirl it through again. Top with the remaining batter.

Step 9

Bake until a toothpick inserted into the center of the cake comes out mostly clean, 1 hour 25 minutes to 1 hour 35 minutes. Meanwhile, clean and dry the stand mixer bowl and whisk attachment. Place 2 ounces cream cheese and 2 tablespoons unsalted butter in the bowl and let sit at room temperature to soften.

Step 10

Let the cake cool in the pan on a wire rack for 10 to 15 minutes, then invert onto a serving plate. Let cool to room temperature, about 90 minutes. Lightly cover the cooled cake with aluminum foil or plastic wrap so it does not dry out if not icing right away.

Step 11

Beat the cream cheese and butter on medium-high speed with the whisk attachment until softened and homogenous, about 2 minutes.

Step 12

With the mixer on low speed, carefully add 1 1/2 cups powdered sugar in 2 batches, scraping down the sides and bottom of the bowl as needed. Once the sugar is fully incorporated, increase the speed to medium-high. Add 1/4 cup milk and 1 teaspoon vanilla extract and beat, adding more milk a teaspoon at a time if needed, until the icing is smooth and pourable.

Step 13

Drizzle the icing over the cooled pound cake. Serve at room temperature.