Preheat oven to 350°F. Grease a 9×5-inch loaf pan with butter or nonstick baking spray or line with parchment paper.
In a large bowl, whisk together eggs, melted butter, Truvia Sweet Complete Granulated Sweetener , Truvia Sweet Complete Brown Sweetener , and vanilla until combined well.
In another bowl, whisk together all-purpose flour, cinnamon, ginger, baking powder, baking soda, and salt.
Gradually mix in the dry ingredients to the wet, just until incorporated. Fold in grated carrots and chopped walnuts.
Pour the batter into the prepared loaf pan and spread evenly. Using a knife, make a shallow cut lengthwise down the center of the batter, about ½ inch deep.
Bake for 50–60 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs. Allow the bread to cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely.
To make the frosting, beat cream cheese, Truvia Sweet Complete Granulated Sweetener, salted butter, salt, and butter on low speed until smooth.
Spread the frosting over the loaf and finish with extra chopped walnuts.