Preheat oven to 375 degrees F. Line a 12-cup muffin tin with paper liners; coat with cooking spray. Set aside. Whisk flour, baking powder, cinnamon, baking soda, ginger and salt in a medium bowl. Whisk eggs, applesauce, brown sugar, granulated sugar and 1/2 cup yogurt in a large bowl; fold in carrots, walnuts and half of the flour mixture until combined. Add the remaining flour mixture; fold until just incorporated (some lumps can remain).
Fill the prepared muffin cups three-quarters full with batter (about 1/3 cup each). Bake until the muffins are golden and a wooden pick inserted in the centers comes out clean, about 18 minutes. Transfer to a wire rack; let cool completely, about 20 minutes.
Whisk confectioners’ sugar, cream cheese and the remaining 2 tablespoons yogurt in a small bowl; whisk in 2 to 3 teaspoons water to reach desired frosting consistency. Dollop and spread the frosting over the cooled muffins.
To make ahead: Wrap airtight and refrigerate for up to 2 days. To freeze, wrap unfrosted muffins tightly in plastic wrap or foil; freeze for up to 3 months. Thaw completely before frosting.