Sift the flour, baking powder, salt and cinnamon into a mixing bowl, then add the sugar.
Peel the bananas and mash them up with a fork in another bowl. Drain and finely chop the pineapple and add to the bananas with the oil, eggs and vanilla extract. Mix until combined, then fold into the dry mixture until smooth.
Finely chop the pecans and gently fold in, then divide the batter evenly between your prepared tins. Bake for 35 to 40 minutes, or until risen, golden and the sponges spring back when touched lightly in the centre.
Run a knife around the edge of the tins, then leave to cool for 10 minutes before transferring to wire racks to cool completely.
To make the icing, sift the icing sugar into a free-standing electric mixer, add the butter and beat until pale and creamy.
Add the cream cheese, finely grate in the zest of 1 lime and add a squeeze of juice, then beat until just smooth – it’s really important not to over-mix it. Keep in the fridge until needed.
Add the pecans and a pinch of salt, spoon around to coat, and when nicely golden, pour onto a sheet of oiled greaseproof paper to set.
Once cool, smash up to a dust (you’ll need about half to top the cake – save the rest for sprinkling over ice cream.
To assemble the cake, place one sponge on a cake stand and spread with half the icing. Top with the other sponge, spread over the rest of the icing, then grate over the zest of the remaining lime.