Courgette and banana sheet cake with caramel buttercream

Ingredients

• 115 g butter at room temperature
• 1 cup sugar
• 1/2 cup brown sugar
• 1 cup mashed ripe banana (approx 2 medium-sized)
• 1/3 cup yoghurt (see notes)
• 1 egg
• 2 tsp vanilla extract
• 3 loose cups grated courgette (approx 2 medium-sized), squeezed of excess juice
• 2 tbsp milk
• 1 tsp baking soda
• 2 cups plain flour
• 1 tsp baking powder
• pinch of salt
• 1 tsp mixed spice
• 1/2 tsp cinnamon
• Caramel buttercream icing
• 100 g butter, at room temperature
• 2 1/2 cups icing sugar
• 3 tbsp caramel
• 1 tbsp milk, if needed