Preheat oven to 175°C. In a large bowl, whisk the eggs.
Add in the yogurt and whisk again until smooth and fluffy.
Pour in the agave syrup, milk, and vanilla extract. Beat the mixture again until smooth.
Add the flour, baking powder, cinnamon, ginger, nutmeg and salt over the wet ingredients. Using a rubber spatula, fold the wet and dry ingredients together just until combined. Lastly, add the shredded carrots.
Scoop the batter into a greased cake tin. Bake for 45-50 minutes.
For the frosting, mix the yoghurt, powdered sugar and vanilla and mix untill well combined.
Once the cake is cooled, use a spoon to put a bit of the frosting on top.
Top it of with some crushed pecan nuts.