Preheat the oven to 350 F. Line a loaf pan with parchment paper.
Using the small holes of a box grater, grate the carrots. You should have about 2 cups of grated carrots. Add them to a large bowl.
Add the Greek yogurt, eggs, olive oil, maple syrup, and vanilla extract to the bowl with carrots. Whisk to combine.
In a separate smaller bowl, add the flour, cinnamon, baking powder, baking soda, and salt. Mix to combine.
Pour the dry ingredients into the bowl with the wet ingredients and mix until just combined, making sure not to over mix.
Finely chop the walnuts. Add the walnuts to the bowl - reserving some for the top of loaf - and gently fold in.
Pour the mixture into the loaf pan, using a spatula or spoon to spread it evenly. Add the remaining walnuts on top and gently press them down. Bake in the preheated oven for 45-50 minutes, or until a knife inserted in the center comes out clean.
Let the loaf cool and make the glaze. Add the powdered sugar, maple syrup, and milk to a bowl and mix until smooth.
Once the loaf has cooled completely, add the glaze on top and cut into slices.