Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a mixing bowl, beat the eggs and sugar until light and fluffy.

Fold in the mashed bananas and vanilla extract gently.

In another bowl, combine the flour, baking powder, baking soda, and salt. Gradually add this to the banana mixture.

Spread the batter evenly onto the lined baking sheet.

Bake for about 15-20 minutes, or until the cake springs back when gently pressed.

Once baked, remove the cake from the oven and immediately dust with powdered sugar (optional).

Invert the cake onto a clean kitchen towel sprinkled with powdered sugar.

Carefully roll the cake and towel together from one short end, then let it cool completely.

Prepare your filling of choice (like whipped cream) and unroll the cooled cake, spreading the filling evenly.

Re-roll the cake with the filling inside, wrapping it tightly in parchment paper or plastic wrap.

Chill the rolled cake in the refrigerator for at least 30 minutes before slicing.

Slice and serve your banana roll cake decorated with additional powdered sugar if desired.