Preheat your oven to 375°F (190°C). Line a rimmed baking sheet with parchment paper, ensuring it extends over the edges for easy removal later.
In a large mixing bowl, whisk together the 3 large eggs and 3/4 cup granulated sugar until the mixture is thick and pale, about 5 minutes. The mixture should form ribbons when you lift the whisk.
Gently fold in the 1 tablespoon of vegetable oil and 1 teaspoon of vanilla extract into the egg mixture.
In a separate bowl, whisk together the 3/4 cup all-purpose flour, 1 teaspoon baking powder, and 1/4 teaspoon salt. Gradually fold this dry mixture into the egg mixture until just combined. Be careful not to overmix.
Divide the batter evenly into small bowls and add food coloring to each bowl to create your desired colors. Gently fold the colors into the batter to create a marbled effect.
Pour the colored batter into the prepared baking sheet, spreading it evenly. Bake for 12-15 minutes, or until the cake is lightly golden and springs back when touched.
Once baked, sprinkle powdered sugar over a clean kitchen towel. Carefully invert the cake onto the towel, peeling away the parchment paper. Roll the cake tightly in the towel, starting from one short end. Allow it to cool completely in the towel.
In a mixing bowl, beat the 1 quart heavy whipping cream until soft peaks form. Gradually add the 2 tablespoons of powdered sugar and the instant vanilla pudding mix, and continue to beat until the mixture is thick and fluffy. Add food coloring to the whipped cream to create a colorful filling.
Unroll the cooled cake carefully and spread the colorful whipped cream filling evenly over the surface. Roll the cake back up tightly, this time without the towel. Wrap it in plastic wrap and refrigerate for at least 1 hour.
Remove the cake roll from the refrigerator, slice off the ends for a clean look, and transfer it to a serving plate. Top with assorted sprinkles, colorful marshmallows, or candies for that magical touch. Slice and serve with joy!
