Wash, peel, and grate (or shred) your carrots. I got lazy and shredded mine in a food processor instead of grating them by hand.
In a large bowl, combine the sugar and softened butter, and cream together until the mixture becomes a pale yellow. Stir in the eggs and vanilla.
In another bowl, combine the flour, cinnamon, baking soda, and salt. Whisk together.
Combine the dry ingredients in with the wet ingredients along with the carrots, cashews, and Greek yogurt. Stir until just combined. Spoon the batter into a buttered baking dish. Bake at 325°F for 55-60 minutes. Allow to cool for 10 minutes before removing from the pan.
For the glaze (if using), whisk together 1/2 cup powdered sugar and 2-3 tablespoons milk. Pour over the still warm loaf just before serving.