Preheat an oven to 190 C / Gas 5. Grease 2 mini-muffin trays or 1 standard muffin tray.
In a mixing bowl, cream together the butter and brown sugar until smooth. Mix in the mashed bananas, squash, carrots and eggs. Stir in the flour, oat bran, bicarbonate of soda, allspice and salt until just combined. Spoon the mixture equally into the prepared muffin tray.
Bake in the preheated oven until a skewer inserted into the centre comes out clean, 15 to 20 minutes. Cool in the tin for 10 minutes before removing to cool completely on a wire rack. Store at room temperature for up to two days, or freeze.