Cream the butter until light and fluffy. Add the bananas and mix well. Mix in the eggs and vanilla.
Sift together the flour, bicarbonate of soda, salt, ground nutmeg and ground cinnamon. Add the dry mixture to the creamed mixture and mix well. Stir in the oats and the chopped nuts. Cover and chill dough for 1 hour.
Preheat the oven to 190 degrees C. Lightly grease baking trays.
Drop chilled teaspoon-sized rounds of biscuit dough onto the prepared baking tray. Bake in the preheated oven for 10 to 12 minutes.