Preheat your oven to 350 degrees F. Grease and flour two 8-inch cake pans.
In a medium mixing bowl, stir together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger until well combined. Set aside.
In a large mixing bowl, beat together the oil and sugar until combined. Add the eggs and vanilla; mix until completely incorporated. Add the sour cream and mix until smooth.
Add half of the dry ingredients to the wet ingredients and mix until just combined. Add the pineapple juice and mix. Add the rest of the dry ingredients, and mix until just combined.
Stir in the carrots and chopped pecans with a wooden spoon until evenly incorporated into the batter.
Pour the batter into the prepared cake pans, half in each pan. Smooth into an even layer and tap the pan on the counter to help remove any air pockets.
Bake for 35 to 40 minutes, or until the edges pull away from the pan slightly and a toothpick inserted in the center comes out clean.
Carefully remove the cakes from the oven. Cool for 10 minutes in the pans, and then transfer to a wire rack to cool completely. (If you have trouble getting the cakes out, you can let them cool in the pans the whole time so they don't break.)
In a medium mixing bowl, beat together the cream cheese, butter, and vanilla until combined.
Add the powdered sugar and beat until smooth. If the frosting it too thick, add 1 tablespoon milk and beat the frosting again. If it's still too thick add another 1 tablespoon of milk and beat until smooth.
Level each of the cakes. Place one cake layer, cut side up, on a cake plate. over the top of the cake in a layer of frosting. (Don't be shy with the frosting.)
Place the second cake layer on top of the first, cut side down, so that you have a flat top to the cake.
Frost the tpo and sides of the cake with the remaining frosting.
Place 12 pecan halves evenly around the outer edge ot the cake top.
Refrigerate until ready to serve.
If you want to make your cake look a little fancier, you can coat the sides with chopped pecans as well.If you're into raisins and/or pineapple in your carrot cake, you can add an 8-ounce can of crushed pineapple that has been drained, and 1/2 cup raisins to the batter when you add in the carrots & pecans.