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Heat oven to 180C/fan 160C/gas 4. Line a 900g/2lb loaf tin with non-stick baking paper, using a little oil to make it stick. Put the dates into a small pan with 200ml boiling water and simmer for 5 mins. Drain the liquid into a jug, then put the dates into a food processor. Add the bananas and 100ml of the date liquid and whizz until smooth. Mix the nuts, dried fruit, polenta, spice and baking powder in a bowl, then add the date purée and rum, and stir until combined.
Whisk the egg whites to soft peaks and fold into the cake mix. Tip into the tin (it will be quite full), then top with the remaining pecans and the banana chips and sugar, if using. Bake for 1 hr until golden and crusty and a skewer comes out clean. Cool completely before cutting into slices.