Make the Cake

Preheat the oven to 350°F. Line a 9x13-inch baking pan with parchment paper, leaving enough overhang on the sides to create a sling for easy removal.

In the bowl of a stand mixer, cream together the softened butter, granulated sugar, and ⅓ cup of the brown sugar until light and fluffy, about 2–3 minutes.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla bean paste.

In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.

With the mixer on low speed, add half of the flour mixture. Mix just until combined.

Add all of the sour cream and mix until incorporated.

Finish by adding the remaining flour mixture, mixing only until no dry streaks remain.

In a small bowl, combine the remaining ⅔ cup brown sugar with the cinnamon.

Spread half of the cake batter into the prepared pan.

Sprinkle half of the cinnamon-sugar mixture evenly over the batter.

Carefully spread the remaining batter over the top. Since the batter is thick, an offset spatula—or even the back of a spoon—works well.

Sprinkle the remaining cinnamon-sugar mixture over the top.

Using a butter knife, skewer, or thin spatula, gently swirl the cinnamon mixture throughout the batter using large figure-eight motions.

Bake for 45 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs but no wet batter.

Cool completely before glazing.

Make the Cream Cheese Glaze

In a medium bowl, beat together the softened cream cheese, powdered sugar, vanilla bean paste, pinch of salt, and milk until smooth.

Add additional milk, one tablespoon at a time if needed, until the glaze is thick but easily pourable.

Pour the glaze evenly over the cooled cake.

Finish with a light sprinkle of turbinado sugar and a dusting of cinnamon.