Preheat the oven to 180°C/350°F/Gas mark 4. Grease 2 x 20cm/8in round cake tins.
Sift together the dry ingredients into a large mixing bowl.
Blend the oil, eggs, milk and vanilla essence until smooth in a separate bowl, then stir in the bananas. Add to the dry ingredients and stir well.
Pour equal amounts into the prepared tins. Bake for 20 minutes, then cool completely on a wire rack. Sprinkle with the caster sugar. Turn one of the cooled cakes upside down, and spread the yogurt on its bottom side. Put the other cake on top, right side up, to make a sandwich.