Preheat oven to 350°F. Line a 12-cup muffin tin with paper liners; lightly coat the liners with cooking spray.
Whisk 1 cup all-purpose flour, 1 cup whole-wheat flour, 1 tablespoon baking powder, 1 tablespoon cinnamon, 1 teaspoon baking soda, ¼ teaspoon nutmeg and ¼ teaspoon salt in a large bowl.
In a separate large bowl, whisk 2 eggs, 1¼ cups yogurt, the mashed banana, ⅓ cup brown sugar, 2 tablespoons oil and 1½ teaspoons vanilla until combined.
Add the flour mixture and whisk just until combined. Fold in 1 cup carrot, ½ cup raisins and ½ cup walnuts until evenly distributed.
Divide the batter evenly among the prepared muffin cups (about ⅓ cup each). Bake until a wooden pick inserted in the center comes out clean with a few moist crumbs attached, about 20 minutes.
Let cool in the pan for 5 minutes, then transfer to a wire rack. Cool completely, about 30 minutes, before frosting.
To prepare frosting: Beat softened cream cheese and 3 tablespoons yogurt in a medium bowl with an electric mixer on medium speed until smooth, 1 to 2 minutes.
Add 2 teaspoons honey and ¾ teaspoon vanilla; beat until smooth, scraping down the sides as needed.
Spread about 1 tablespoon frosting over each cooled muffin. Dust with additional cinnamon, if desired.
