Preheat oven to 425 degrees.
Shred the carrots in a food processor (affiliate link) or grate them on a box grater. Set aside.
To a large bowl, whisk together the flour, brown sugar, baking soda, baking powder, salt, cinnamon, ginger and nutmeg. Add the shredded carrots and mix with a spoon to combine.
To a large measuring cup (affiliate link and my favorite), whisk together the liquid ingredients: vegetable oil, plain yogurt, eggs and vanilla extract.
Pour the liquid mixture on top of the flour/carrot mixture and gently stir to combine. Add 3/4 cup chopped fruit, nuts or a combination of both if desired.
Line a 9 by 5 loaf pan with parchment paper or use a good quality non-stick loaf pan (affiliate link).
Spread the carrot cake loaf batter into the prepared pan. Bake for 10 minutes at 425 degrees. Then reduce the temperature to 350 degrees and continue baking for 45-50 minutes. Insert a toothpick or sharp knife in the center to check for doneness. If it comes out "clean" with no crumbs, it is ready. If it comes out wet, let it bake for another few minutes and check again.
While the loaf cools, prepare the cream cheese topping.