For the cupcakes: Position a rack in the center of the oven and preheat the oven to 350 degrees F. Line a 12-cup muffin tin with paper liners.
In a medium bowl, whisk together the flour, baking powder, cinnamon, nutmeg, baking soda, salt and ginger.
In a separate medium bowl, whisk together the sugar, yogurt, oil, vanilla extract, banana, carrots, and egg. Pour the wet ingredients into the dry and fold to blend well. Fill the cups of the muffin tin about halfway with the batter. Bake until a toothpick inserted in the center comes out clean and the tops of the cupcakes spring back when lightly pressed, 15 to 20 minutes.
Cool in the pan for 3 minutes before removing to a wire rack to cool completely (cooling the cupcakes in the pan completely will make them tough).
For the frosting: In the heatproof bowl of a stand mixer fitted with the whisk attachment, combine the sugar, salt and egg whites. Place the bowl over a saucepan of gently simmering water to create a double boiler (make sure there is space between the water and the bottom of the bowl). Whisking by hand, heat the mixture until slightly thickened, a bit lighter in color and hot to the touch; a candy thermometer dipped into the mixture should reach 160 degrees F (very important so that the frosting will whip up firmly!). Return the bowl to the stand mixer. Whip the mixture on high speed until very thick, fluffy and pale latte in color, 5 to 10 minutes depending on your mixer. The frosting is done when it's very stiff and the bowl is completely cool to the touch all over.
Top the cooled cupcakes with 2 tablespoons frosting per cake. Dust lightly with ground cinnamon to garnish. Refrigerate any leftovers in an airtight container for up to 2 days.