Preheat oven to 450 degrees Fahrenheit. Line 12x17 pan with parchment paper or spray with non-stick spray.
Mix 2 whole eggs, 3 egg yolks and ½ cup sugar on medium speed for 5 minutes until it turns pale yellow and thickens.
Add 1 teaspoon vanilla, several drops of green food coloring, ⅓ cup flour and 3 tablespoons of cornstarch. Fold together until well combined.
In a separate bowl, combine 3 egg whites and 1 tablespoon of sugar. Whip on high for 2 - 3 minutes.
Combine whipped egg whites with cake batter and gently fold together.
Pour batter into cake pan and bake for 8 - 10 minutes. Center should be set and cake should be light brown.
Allow cake to cool for 5 - 10 minutes.
Sprinkle cake with thin layer of powdered sugar and top with parchment paper 2 inches larger than cake.
Flip cake so that it is on the new parchment paper on the counter and carefully remove pan.
Sprinkle cake with another light layer of powdered sugar. Then roll cake up so that the parchment paper is rolled with it.
Allow cake to continue cooling.
Add 1 cup butter, 1 teaspoon vanilla and 3 cups powdered sugar to a mixing bowl and combine on low speed.
Once everything in combined, bump speed to medium for another 2 - 3 minutes or until it is smooth and fluffy.
Once cake is totally cooled, unroll and spread frosting on top.
Carefully reroll cake as tightly as possible without the parchment paper.
Chill cake for at least 30 minutes.
In a microwave safe bowl, add 1 cup green candy melts and 3 tablespoons of heavy cream. Heat in microwave at 30 second intervals until melted.
Pour green ganache over top of the cake roll using a spatula to spread it out evenly.
Sprinkle red heart sprinkles on top for decoration.