Preheat oven to 350 F°. Line 12 standard cupcake cups with paper liners, set aside.
For icing, start with a small saucepan, melt white chocolate over low heat. Stir until smooth, and allow to cool to room temperature.
In a bowl, beat together the cream cheese and butter until smooth. Mix in white chocolate, 1 teaspoon vanilla, and orange extract. Gradually beat in the confectioners’ sugar until the mixture is fluffy. Mix in heavy cream.
For cupcakes, beat together the eggs, white sugar, and brown sugar in a bowl, then mix in the oil and vanilla. Fold in mashed carrots. In a separate bowl, mix the flour, baking soda, salt, cinnamon, nutmeg, and ginger. Mix flour mixture into the carrot mixture until evenly moist. Fold in 1/2 cup walnuts. Transfer to the prepared cupcake cups.
Bake 25 minutes in the preheated oven, or until a toothpick inserted in the center of a cupcake comes out clean. Cool completely on wire racks before topping with the icing and sprinkling with remaining walnuts.