Preheat the oven to 350F. Line 12 x 16 jelly roll pan with parchment paper.

1. Mix eggs and egg yolk; add sugar, beating continuously.
2. Beat for 5-6. min. 
3. Sift in flour together with baking powder.
4. Slowly add in oil.  
5. Turn off the mixer, add dry ingredients and mix until all ingredients are well blended.
6. Spread batter in the prepared pan. Bake for 12 minutes. Put the pan on the rack to cool.
7. Pour about a half of the prepared milk into a medium saucepan. Add sugar and vanilla sugar.
8. Pour another half into a medium bowl, add pudding and mix well. 
9. Bring the milk in the saucepan to boil.  Add in pudding mix and cook mixing continuously until thickened. 
10. Remove from heat, put clear wrap directly over cooked pudding and leave to cool.
11. Once completely cooled, transfer to a mixing bowl and mix well until smooth. 
12. Add softened butter little by little into the pudding mixture and mix until well blended. 
13. Spread pudding cream over cake, leaving little for the top and sides of the cake roll.  
14. Cut the corners of bananas and then line them up along the longer end.
15. Roll it up, spread remaining cream over.
16. Mix heavy whipping cream with powdered sugar until stiff peaks.
17. Spread over the roll. Sprinkle with melted chocolate or some other decorations of your choice.