Preheat the oven to 180c (350f). Butter the bundt cake pan with room-temperature butter and flour to prevent the cake from sticking to the pan.
Into a large mixing bowl, add the eggs, yogurt (or sour cream), sugar, brown sugar, cinnamon, nutmeg, vegetable oil, kosher salt, vanilla extract, and mix with a whisk until well combined.
Add the grated carrots and mix with a whisk until well combined.
Add the flour, baking soda, and baking powder, and mix until just combined. Do not overmix.
Pour the batter to the prepared cake pan and bake in a 180c (350f) oven for about an hour or until a toothpick inserted into the cake comes out clean.
Allow the cake to cool to room temperature before flipping the cake. Top the pan with a plate, flip the cake and tap the cake pan to release the cake from the pan.
In a medium-sized bowl, add the softened cream cheese, softened butter, powder sugar, and vanilla extract. Mix with a spoon or a tiny whisk until creamy and smooth.
Top the cake with the glaze and let it sit for a few minutes before serving. Enjoy!