Preheat your oven to 350°F (175°C). Prepare a 15x10 inch jelly roll pan by lining it with parchment paper and giving it a light greasing to prevent sticking.
In a large mixing bowl, beat together the eggs and granulated sugar using an electric mixer on medium speed until the mixture is light, fluffy, and has doubled in volume—this should take about 2-3 minutes.
In a separate bowl, sift together the all-purpose flour, baking powder, cocoa powder, and salt to ensure there are no lumps and the ingredients are well combined.
Gradually incorporate the dry ingredients into the egg mixture, alternating with the vegetable oil and vanilla extract. Mix gently until just combined, being careful not to overmix.
Stir in the red food coloring until the batter is evenly tinted throughout, creating that vibrant red color characteristic of red velvet.
Pour the prepared batter into the lined jelly roll pan, using a spatula to spread it evenly across the surface. Bake in the preheated oven for 12-15 minutes, or until a toothpick inserted in the center comes out clean.
While the cake bakes, prepare a clean kitchen towel by generously dusting it with powdered sugar to prevent sticking.
Upon removing the cake from the oven, immediately invert it onto the prepared towel. Carefully peel off the parchment paper while the cake is still warm.
Roll the cake tightly, starting from one of the shorter edges, using the towel to help guide it. This helps create the rolled shape and allows it to cool while maintaining form.
Once rolled, set the cake aside to cool completely in this rolled position.
For the cream cheese filling, beat the softened cream cheese and butter in a large mixing bowl until the mixture is smooth and creamy. Gradually add in the powdered sugar and vanilla extract, mixing on low speed until fully combined and fluffy.
Once the cake is completely cooled, gently unroll it and spread the cream cheese filling evenly over the surface of the cake, leaving about a half-inch border.
Carefully re-roll the cake without the towel, ensuring the seam is on the bottom. Wrap the rolled cake tightly in plastic wrap and refrigerate for at least 1 hour to set.
Just before serving, dust the top of the cake roll with additional powdered sugar for an elegant finish. Slice into 8-10 servings, and enjoy the festive treat!