Preheat the Oven: Set your oven to 350°F (175°C). Line a 9x13-inch baking pan or sheet pan with parchment paper or lightly grease it.
Make the Batter: In a large bowl, cream together the butter and sugar until light and fluffy. Add the sour cream and stir to combine. Mix in milk, then beat in the eggs and vanilla extract until smooth.
Add Dry Ingredients: In another bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, stirring until the batter is smooth and uniform.
Prepare the Cinnamon Swirl: In a small bowl, combine brown sugar, cinnamon, and melted butter. It should form a rich, pourable paste.
Layer the Cake: Pour half the batter into your prepared pan. Drizzle half the cinnamon mixture over it. Add the remaining batter, then top with the rest of the cinnamon swirl. Use a knife or skewer to gently marble the layers — don’t overmix.
Bake: Bake for 23–25 minutes, or until a toothpick inserted in the center comes out clean. The top should be golden brown and fragrant.
Make the Glaze: In a small saucepan, combine butter, granulated sugar, heavy cream, vanilla, and corn syrup. Bring to a gentle boil for 3–4 minutes, stirring constantly. Remove from heat, stir in the cream cheese until melted, then gradually whisk in powdered sugar until smooth.
Finish & Serve: Pour the warm glaze over the slightly cooled cake. Let it soak in for a few minutes, then slice into squares and serve warm.