For the cake: Preheat the oven to 350 degrees F. Spray 12 mini loaf pans or a 12-cup regular muffin pan with pan release spray.
Spread the pecans out on a rimmed baking sheet and bake until toasted, 10 to 12 minutes. Allow to cool and then pulse in a food processor until very finely chopped but not ground.
Combine the chopped pecans, flour, baking powder, cinnamon, ginger, baking soda and salt in a large bowl. Whisk together the brown sugar, yogurt, oil, vanilla extract, lemon zest and eggs in another bowl. Stir the carrots into the egg mixture. Fold the carrot-egg mixture into the flour mixture until just combined. Divide evenly among the prepared pans. (Don't be alarmed if the batter seems skimpy; the cakes will rise once baked.)
Bake until the center of the cakes bounce back when pressed and a toothpick inserted in the middle comes out clean, 20 to 22 minutes. Let the cakes cool in the pans for a few minutes, and then transfer to a rack to cool completely.
For the glaze: Mix together the confectioners' sugar, cream cheese, lemon juice, vanilla extract and salt in a medium bowl. Spoon about 1 teaspoon of the glaze onto each cake and use the back of the spoon to spread. Garnish as desired.
Per Serving: Calories: 240; Total Fat: 11 grams; Saturated Fat: 2 grams; Protein: 5 grams; Total carbohydrates: 31 grams; Sugar: 17 grams; Fiber: 3 grams; Cholesterol: 49 milligrams; Sodium: 316 milligrams