Whisk together the milk, corn oil and liquid red food coloring, then beat with a mixer until well combined.
Sift in the cocoa powder and mix well. Adding just a little cocoa powder will give the sponge a deep, intense red color.
Separate the egg whites from the yolks. Add the yolks to the batter and mix until fully incorporated.
In a clean, dry bowl, combine the egg whites with a little lemon juice. Then add the granulated sugar and continue beating until stiff peaks form.
In several additions, gently fold the whipped egg whites into the batter, mixing carefully after each addition.
Pour the batter into a 11 x 11-inch (28 x 28 cm) baking pan lined with parchment paper, then tap the pan lightly so the batter spreads evenly. Bake at 340°F (170°C) for about 20 minutes, turning on convection for the last 5 minutes.
Carefully lift the sponge out of the pan with the parchment paper and let it cool completely.
Trim any uneven edges, then toast the trimmings at 300°F (150°C) for about 10 minutes. Let them cool and crumble for decoration.
Beat the room-temperature cream cheese with vanilla until smooth.
Whip the heavy cream with powdered sugar to stiff peaks, then fold in the cream cheese mixture until smooth.
Reserve about 1/3 cup (80 g) of cream for decorating. Spread the remaining cream over the sponge, leaving a small border at the edges. Roll up and chill for at least 30 minutes.
Decorate the chilled roll with the reserved cream, fresh berries or fruit, and the red sponge crumbs.