Heat the oven to 180C/fan 160C/gas 4, and line the base and sides of a deep 20cm (8 inch) loose-bottomed cake tin with baking parchment. For the crumble topping stir together 2 tbsp each of the sugar, flour and chopped pecans, then add the butter, cut into a few pieces, and rub together until you have sticky crumbs. Set aside.
Break up the whole eggs with a fork, then mix with the mashed banana, oil and milk until all the wet ingredients are well combined. In a separate, large bowl tip in the remaining sugar, flour and pecans, and briefly stir with the cinnamon and baking powder. Whisk the egg whites until just stiff. To combine, tip the oily banana mixture into the bowl of dry ingredients and quickly stir in until you have a smooth, lump-free mix. Finally using a large metal spoon or spatula gently fold in the egg whites, then carefully pour the mixture into the prepared tin. Scatter over the crumble topping and bake for 1 hr, until a skewer stuck in to the middle comes out clean. Check the cake with 15 mins to go, if the surface is browning too quickly cover with another piece of baking parchment.
Once the cake is ready leave it in its tin for 5 minutes, then finish cooling on a wire rack.