Prep the pan: Heat oven to 350°F (175°C).
Line a 12-cup muffin tin with paper liners or grease well. For toddlers, mini muffins also work great; use two mini pans if you have them.
Mash bananas: In a large bowl, mash the ripe bananas with a fork until mostly smooth. A few small lumps are fine.
Add wet ingredients: Whisk in the eggs, yogurt, oil, and vanilla until combined.
Stir in the grated carrot.
Combine dry ingredients: Sprinkle the flour, oats, baking powder, baking soda, cinnamon, and salt over the wet mixture. Gently fold until just combined. Do not overmix.
Add optional mix-ins: If using raisins, ground flax, or chia, fold them in now.
The batter will be thick.
Fill the cups: Divide the batter evenly among the muffin cups, filling each about 3/4 full. For mini muffins, fill just to the top.
Bake: Bake standard muffins for 18–22 minutes, or mini muffins for 12–14 minutes, until a toothpick comes out clean or with a few moist crumbs.
Cool: Let muffins cool in the pan for 5 minutes, then transfer to a wire rack to finish cooling. This helps them set and stay moist.
Serve: For younger toddlers, you can break muffins into small pieces and serve with a thin smear of yogurt or nut/seed butter.