In a standing mixer with the paddle attachment, combine 1 cup granulated sugar, 1 cup brown sugar and 1 cup melted butter. Mix until thoroughly combined.
Add in 1/2 cup Greek yogurt, 5 eggs & 1 tsp vanilla
In a separate bowl combined all dry ingredients (3 cups all-purpose flour, 1 tsp baking soda, 1 1/2 tsp baking powder, 1 tsp fine sea salt, 2 tsp ground cinnamon, 1/2 tsp nutmeg)
Turn the mixer on low and slowly pour in half of the dry ingredients
Alternate and pour in half of the 3 1/2 cups grated carrots
Repeat adding the rest of the dry ingredients & then the rest of the carrots. Mix until fully combined
Spray and line cake pans with nonstick spray and parchment paper. Pour half the batter into a 9" round pan and the other half into a second 9" round pan
Bake for 25-30 minutes until no longer giggly in the middle of the cake
Frosting
In a standing mixer with the paddle attachment, combine butter and cream cheese, whip until softened
Add in powdered sugar and vanilla, whip on medium high speed for 2 minutes until lighter in color and texture
Assemble
After cake is fully cooled, wrap in plastic wrap and allow to get chilled in the freezer for at least 15 to 30 minutes.
Remove from freezer and frost with a thin layer of frosting, filling between each layer of cake with a more healthy portion of frosting.
Place the cake back into the freezer to freeze any crumbs into that first thin layer of frosting
Take the cake out of the freezer and use the rest of the frosting the cover the cake