Preheat Oven:
Preheat to 350°F (175°C).
Grease and flour a 9x13-inch baking dish.
Mix the Cake Batter:
In a large bowl, beat together cake mix, mashed sweet potato, sour cream, oil, eggs, vanilla, cinnamon, and nutmeg until smooth and well combined.
Make the Swirl Mixture:
In a small bowl, mix brown sugar and cinnamon.
Assemble the Cake:
Pour half of the batter into the prepared pan and smooth it out.
Sprinkle the cinnamon-sugar swirl evenly over the batter.
Top with the remaining cake batter and gently swirl with a knife if desired (or leave layered for a distinct ribbon).
Bake:
Bake for 35–40 minutes, or until a toothpick inserted in the center comes out clean.
Let cool slightly before glazing.
Make the Glaze:
In a small bowl, whisk together powdered sugar, milk, and vanilla until smooth.
Drizzle over the warm cake and let it set.