Preheat oven to 350°F (180°C). Line a 12-cup muffin pan with paper liners or lightly grease.
Spread walnuts on a baking sheet and toast for 5 minutes at 350°F (180°C). Allow to cool slightly, then roughly chop them.
In a large bowl, whisk together flour, baking powder, baking soda, cinnamon, ginger, nutmeg, salt, and sugar until combined.
In another bowl, whisk together eggs, mashed bananas, melted butter, avocado oil, and vanilla until smooth.
Add the wet ingredients to the dry ingredients, stirring gently until just combined.
Gently fold in shredded carrots and ¾ cup of toasted walnuts.
Divide batter evenly into the muffin cups, filling each almost to the top. Sprinkle remaining walnuts on top.
Bake for 22 minutes, or until muffins rise and a toothpick inserted in the center comes out clean.
Allow muffins to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.