Mix egg yolks with sugar until pale. Add vanilla extract, egg whites and flour-cocoa mixture. Slowly and gently stir with a spoon (do not use mixer).
Transfer the mixture to a sheet pan lined with baking paper (my pan is 12x13 inches or 30x33 cm large). Bake in 180 C (350 F) oven for about 15 minutes.
FILLING: Mix eggs with sugar over water bath (or a very low heat). Cook until mixture reaches 80 C (175 F). Be careful, because if you continue cooking over this temperature, the eggs will coagulate (scramble).
Mix butter until fluffy. Combine butter with egg-chocolate mixture.
ASSEMBLING: Peel off the baking paper from the sponge. Place on a cling film (it will help you roll the cake easier). Spread the cake with 1/2 of the chocolate filling. Place two bananas on 2 opposite sides of the cake. Slowly roll each end toward center (see video).
OPTIONAL STEP: Before serving, take the cake out of refrigerator and let come to room temperature. Whip cream until stiff. (If cake will wait for your guests for longer time, consider stabilizing whipped cream.) Sprinkle with chocolate sprinkles.