Preheat the oven to 350 degrees. Grease and "flour" (with cocoa powder) a 10 or 12 cup bundt pan (This is important, as bundt cakes can be tough to remove from their pans, if the pan is not properly prepared). Set aside.

Combine the flour, cocoa powder, baking powder, baking soda, and salt in a medium bowl and whisk long enough to ensure the leavening is evenly distributed. Set aside. In a large bowl, combine the sugars and oil and whisk vigorously. Add the yolks and eggs, one at a time, gently whisking after each addition. Add the buttermilk and vanilla and whisk again. Add the melted chocolate and whisk a final time.

Add the flour mixture to the egg and sugar mixture, and with a rubber spatula, gently fold the dry into the wet, until a few streaks of flour remain. Add the carrots and fold again, until the carrots are completely incorporated. let the cake batter rest for 15 minutes.

Transfer the batter to the prepared bundt pan and bake for 45 to 50 minutes, rotating the cake after 20, and checking it with a cake tester/toothpick after 40. The tester should have a few moist crumbs, on it, but nothing too wet.

Remove the cake from the oven and let it rest in its pan on a cooling rack for about 20 minutes or so, or until the cake is still warm and you can easily hold the pan without burning yourself. Run a knife around any edges of the cake that seem to be sticking to the pan and invert the cake onto the cooling rack, giving it a good whack if necessary.

Let the cake cool completely and serve dusted with confectioners' sugar or with the cream cheese frosting (tinted orange) of your choosing.

The cake will keep tightly covered in plastic wrap on the counter for up to 3 days.