Step 1: Preheat your oven to 375°F (190°C). Grease a 15x10-inch jelly roll pan, then line it with parchment paper, allowing an overhang on the longer sides. Grease the parchment paper as well.
Step 2: In a medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking soda, and salt. Set aside.
Step 3: In a large bowl, using an electric mixer, beat the eggs with granulated sugar on high speed until light and fluffy, about 3-5 minutes. Beat in the vegetable oil and 1 teaspoon vanilla extract. Add the red food coloring and mix until fully incorporated.
Step 4: Gradually add the dry ingredient mixture to the wet mixture, alternating with the buttermilk, beginning and ending with the dry ingredients. Mix on low speed just until combined; do not overmix.
Step 5: Pour the batter evenly into the prepared jelly roll pan, spreading it to the edges with an offset spatula. Bake for 12-15 minutes, or until a toothpick inserted into the center comes out clean and the cake springs back when lightly touched. Do not overbake.
Step 6: While the cake is baking, lay a clean kitchen towel on your counter and dust it generously with powdered sugar. Immediately upon removing the cake from the oven, invert it onto the powdered sugar-dusted towel. Carefully peel off the parchment paper. Trim off any crisp edges of the cake (about 1/4 inch).
Step 7: Starting from a short end, carefully roll the warm cake (along with the towel) into a tight spiral. Place the rolled cake, seam-side down, on a wire rack and let it cool completely to room temperature, which will take about 1 hour.
Step 8: While the cake cools, prepare the filling. In a medium bowl, beat the softened cream cheese, softened unsalted butter, 1 teaspoon vanilla extract, and 1/4 teaspoon salt until smooth and creamy. Gradually add 3-4 cups sifted powdered sugar, beating until light and fluffy. Adjust consistency with more powdered sugar or a teaspoon of milk if needed.
Step 9: Once the cake is completely cool, carefully unroll it. Spread the cream cheese filling evenly over the entire surface of the cake, leaving a 1-inch border at one of the short ends.
Step 10: Starting from the filled short end, carefully re-roll the cake into a tight spiral. Wrap the cake roll tightly in plastic wrap and refrigerate for at least 2 hours, or preferably overnight.
Step 11: Just before serving, unwrap the chilled cake roll and place it on a serving platter. Dust generously with additional powdered sugar for a beautiful finish. Using a sharp, serrated knife, slice the cake into 1-inch thick rounds. Clean the knife between slices for the cleanest cuts.