Preheat oven to 350°F (175°C) and grease an 8x8 inch baking pan.
In a large bowl, whisk together whole wheat flour, baking soda, baking powder, cinnamon, ginger, and salt.
In a separate medium bowl, combine eggs, maple syrup, melted coconut oil, Greek yogurt, and vanilla extract until smooth.
Fold the wet ingredients into the dry ingredients until just combined.
Gently stir in the grated carrots and chopped walnuts.
Spread the batter evenly into the prepared baking pan.
Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bars to cool completely in the pan before slicing into 12 even pieces.