Start by preheating your oven to 350°F (175°C). Get two 9-inch round cake pans ready—either grease and flour them or line them with parchment paper so the cake doesn’t stick.
In a large mixing bowl, combine all the dry ingredients: flour, baking soda, cinnamon, nutmeg, kosher salt, and table salt. Give everything a good whisk so it’s evenly mixed, then set it aside for now.
In a separate bowl, add the softened butter along with both the brown and white sugars. Use a mixer to beat them together until the mixture looks fluffy and pale—that usually takes a few minutes.
Next, add the eggs. Do this one at a time, beating well after each one so everything blends smoothly. Stir in the vanilla extract once all the eggs are mixed in. Now, pour in the canola oil and buttermilk, and mix until the batter looks uniform and creamy.
Take the bowl with the dry ingredients you set aside earlier, and slowly add them to the wet mixture. Stir gently until everything is just combined don’t overmix it.
Now it’s time to fold in the good stuff. Add the grated carrots, grated apple (Granny Smith is best here), chopped pecans, and sweetened shredded coconut. Stir them in evenly. Finally, pour in the melted butter and give it one last gentle mix.
Divide the batter evenly between your two prepared pans. Smooth the tops out a bit, then place them in the oven. Bake for about 45 to 50 minutes. You’ll know they’re done when a toothpick inserted in the center comes out clean.
Once the cakes are baked, take them out of the oven and let them cool in the pans for around 10 to 15 minutes. After that, turn them out onto a wire rack to cool completely.
While the cakes are cooling, make the frosting. Start by browning the butter—put it in a saucepan over medium heat and cook it until it turns golden brown and gives off a nutty smell, which should take about 5 to 7 minutes. Let it cool for a few minutes.
In a large bowl, beat together the softened cream cheese, mascarpone cheese, and that browned butter until it’s all smooth. Gradually add in the powdered sugar, mixing as you go until the frosting is creamy. Add the kosher salt and vanilla (paste or extract), and mix until everything is well combined.
To put the cake together, place one layer on your serving plate. Spread a thick layer of frosting on top. Gently set the second cake layer over it, then frost the top and sides until everything’s evenly covered. If you want, sprinkle on some extra chopped pecans or a little shredded coconut as a finishing touch.