Preheat oven to 350 degrees F (175 degrees C). Lightly grease 12 muffin cups.
In 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.
Beat together the eggs, white sugar, and brown sugar in a bowl, and mix in the oil and vanilla. Fold in carrots and pineapple. 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 muffin cups.
Bake 25 minutes in the preheated oven, or until a toothpick inserted in the center of a muffin comes out clean. Cool completely on wire racks before topping with the icing and sprinkling with remaining walnuts.