Preheat the oven to 350ºF (180ºC).
Line 12 regular muffin tins with paper liners or butter/spray the pans.
Sift together dry ingredients in a large bowl: 1 cup all-purpose flour, 1 teaspoon baking powder, ½ teaspoon baking soda, ½ teaspoon salt, ¼ teaspoon ground cinnamon and ⅛ teaspoon ground ginger. Add ½ cup white sugar and stir to combine. Reserve.
Whisk 1 egg, ⅓ cup vegetable oil and ½ teaspoon vanilla extract in a medium bowl. Do not beat, but mix well until no streaks of egg whites remain.
Add ⅔ cup mashed bananas and stir.
Add the wet ingredients at once to the bowl with the dry ingredients.
Mix until you barely have streaks of flour, but do NOT overmix. It will be lumpy and not completely mixed and that is fine.
Fold in 1 cup grated carrots and integrate with a rubber spatula. Don't overmix.
Divide evenly among the muffin cups or muffin liners.
Bake for 25-30 minutes, until the top is dry and golden brown, and a cake tester or toothpick inserted in the center comes out clean. Don't overbake.
Let cool on a wire rack and eat warm or let cool down completely.
They are best eaten the day they are made, but you can keep them for a day at room temperature covered or wrapped.
Store leftovers, covered in plastic wrap or in an airtight container, in the refrigerator for a few days or frozen for a month.