Preheat the oven to 375F and center the oven racks. Butter two 8-inch cake pans, and line them with parchment paper. Dust the bottoms and sides with flour, and tap out any excess. Set the pans aside.
Grate the carrots using a grater with smaller holes. The grated carrots should yield 2.5 cups. Place the carrots, eggs, buttermilk, vanilla, sugar, oil, and ginger in a large bowl. Whisk until combined.
In another bowl, whisk the flour, baking powder, baking soda, salt, and cinnamon. Using a rubber spatula, fold the flour mixture into the carrot mixture until combined. Fold in the toasted pecans.
Divide the cake batter evenly between the two cake pans. Bake until a toothpick inserted comes out clean, rotating the pans for even baking, if needed, about an hour. Transfer pans to a wire rack to cool for 10 minutes. Remove the cakes from the pans and return the cakes to the pan to cool.
To make the frosting, place the butter in the bowl of an electric mixer fitted with the paddle attachment. Beat on medium-high speed until fluffy, about 2 minutes. Add the cream cheese. Beat until well combined and fluffy, about 2 minutes more. Gradually beat in the sugar on low speed. Then beat in the orange zest, ginger, and a pinch of salt. Beat 5 minutes. Use immediately, or refrigerate and whip again before using.
To assemble, remove the papers from the bottoms of the cakes. If you want to create 4 layers, use a long serrated knife to cut each cake layer in half horizontally. Place a layer on a cake stand and spread 1/4 cup of the frosting across the top. Continue layering the cake and spread the frosting on the top and sides.