Preheat oven to 180° celsius (fan-forced). Grease and line a 30cm x 22cm rectangular baking tin with baking paper. Set aside until needed.
Place the plain flour and baking powder into the Thermomix bowl. Sift using 1 sec, Turbo Function, 5-10 times, then set aside in a separate bowl.
Place the butter, caster sugar, brown sugar and vanilla extract into the Thermomix bowl. Cream for 30 seconds,Speed 4. Scrape down the sides of the bowl and repeat for a further 30 seconds.
Reduce to Speed 2, and with the blades still turning, add the eggs one at at a time. Once combined, mix for 15 seconds, Speed 4.
Add the sour cream and mashed banana and mix for 15 seconds, Speed 4.
Add the plain flour, baking powder and poppy seeds and mix for 15 seconds, Speed 5.
Pour the mixture into the prepared baking tin and bake for 40 minutes, or until cooked through.
Allow the cake to cool in the baking tin for 30 minutes before turning onto a wire rack to cool completely.