Preheat the oven to 180°C. Line a 10–12-hole muffin tin with paper cases.
Mash the bananas in a large bowl.
Add the egg, vanilla extract and oil and whisk together until well combined.
Stir in the grated carrot and chopped peach.
Add the oats, self-raising flour and baking powder. Gently mix until just combined. Do not overmix; the batter should be thick and moist.
Divide the mixture between the muffin cases, filling each about three-quarters full.
Bake for 20–25 minutes, or until the muffins are lightly golden and a skewer inserted into the centre comes out clean.
Leave to cool in the tin for a few minutes, then transfer to a wire rack.