Prepare the Cake Batter

1. Preheat Oven: Preheat your oven to 350°F (175°C). Line a 15×10-inch jelly roll pan with parchment paper, then lightly grease the paper.
2. Mix Wet Ingredients: In a large mixing bowl, beat together the eggs and sugar until light and fluffy, about 2 minutes. Add the milk, vegetable oil, and vanilla extract, and mix until combined.
3. Combine Dry Ingredients: In a separate bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt.
4. Incorporate Dry Ingredients: Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Be careful not to overmix.
5. Pour into Pan: Pour the batter into the prepared jelly roll pan, spreading it evenly to the edges.

Create the Cinnamon-Sugar Swirl

1. Mix Cinnamon-Sugar: In a small bowl, stir together the brown sugar and cinnamon.
2. Add the Swirl: Evenly sprinkle the cinnamon-sugar mixture over the cake batter. Use a butter knife to gently swirl the cinnamon-sugar into the batter, creating a marbled effect.

Bake the Cake

1. Bake: Place the pan in the oven and bake for 12-15 minutes, or until the cake is golden brown and a toothpick inserted in the center comes out clean.
2. Cool the Cake: Remove the cake from the oven and let it cool in the pan for about 10 minutes. While it’s cooling, prepare a clean kitchen towel by sprinkling it lightly with powdered sugar.
3. Roll the Cake: Once the cake has cooled slightly, carefully flip it onto the prepared towel. Peel away the parchment paper, then roll the cake up with the towel inside. Allow it to cool completely in the towel.

Make the Cream Cheese Frosting

1. Prepare Frosting: In a medium bowl, beat the softened cream cheese and butter until smooth and creamy. Gradually add the powdered sugar, vanilla extract, and heavy cream, beating until smooth and fluffy. If the frosting is too thick, add a little more heavy cream to reach your desired consistency.

Assemble the Cake Roll

1. Unroll the Cake: Once the cake is completely cool, gently unroll it from the towel.
2. Frost the Cake: Spread an even layer of the cream cheese frosting over the top of the cake, leaving a small border around the edges.
3. Roll the Cake Again: Carefully roll the cake back up, this time without the towel. Be gentle to avoid cracking the cake.
4. Chill: Place the rolled cake in the refrigerator for at least 30 minutes to set before slicing.