Preheat the oven to 350F. Line a half-sheet pan with parchment paper, leaving the sides ungreased. Prepare the banana cake first. Place the eggs and sugar into a stand mixer bowl and whisk on high speed for 7 to 9 minutes, until the eggs are thick, pale in color and voluminous. Add the banana and vanilla extracts and whisk again for 30 seconds.
In a separate bowl, combine the flour and baking powder. Sift the dry ingredients into the eggs in small portions, folding gently but thoroughly after each addition. Mash the ripe bananas with a fork, then add to the cake batter, along with the chopped pecans. Fold the banana and nuts into the batter for gently, then pour the batter into the prepared pan.
Spread the cake batter evenly to the edges, then bake in preheated oven for 18 to 20 minutes, until the top of the cake is golden brown. Immediately after taking the cake out of the oven, run a knife along the edges to loosen the cake from the pan. Sprinkle a light dusting of confectioner's sugar over the top, cover the cake with a clean tea towel, and invert a cooling rack on top. Using kitchen mitts/towels, invert the cake, then gently lift the pan and pull away the parchment paper. Using the tea towel, roll the cake into a roll and allow to cool completely on a wire rack.
Once cake has cooled completely, prepare the frosting. For the cream cheese frosting, place the softened butter and cream cheese into a mixer bowl. Mix on medium-high speed for 4 to 6 minutes, scraping down the sides of the mixing bowl often, until the mixture is creamy and lump-free. Add the vanilla extract and slowly add in the confectioner's sugar. Once all the sugar has been added, turn the mixer to high speed and mix for a few minutes.
To assemble the cake, gently unroll the sponge cake. Spread two-thirds of the cream cheese frosting onto the cake and use an off-set spatula to spread the frosting evenly to all edges. Top the frosting with sliced fresh bananas. Gently roll the cake back up the same way it cooled and transfer onto a serving tray.
Use the remaining frosting to frost the top and sides of the cake. Garnish the cake with more sliced bananas and mint leaves, if desired. Before adding bananas on top of the cake, brush the banana slices with lemon juice to prevent browning.