In a large bowl, whisk the eggs until light and fluffy. Add in the Greek yogurt and whisk again until smooth and fluffy. Pour in the maple syrup, milk and vanilla extract. Beat the mixture again until smooth.
Add the shredded carrots, whole wheat flour, baking powder and cinnamon to the wet ingredients. Using a rubber spatula, fold the wet and dry ingredients together just until combined.
Using a medium ice cream scoop, portion the batter into a greased 12-cup muffin tin.
Bake for 20 minutes or until a toothpick is inserted into the muffin and comes out clean. Let cool completely.
For the frosting, beat the cream cheese in a small bowl until smooth. Add in the maple syrup and vanilla and beat again until the mixture is well combined.
Use a small spoon with a bit of the frosting on top of the muffins or pipe each top.