Preheat the oven to 350 degrees F. Line a 12 cup muffin pan with paper cupcake liners.
In a large bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, and Chinese five-spice powder.
In another large bowl, whisk together the vegetable oil, crushed pineapple, eggs, sugar, vanilla extract and carrots. Then slowly add the flour mixture and beat with an electric hand mixer until just combined, about 2 minutes.
Fill the cups 3/4 full with batter. Bake until the cupcakes are set, about 20 to 22 minutes. When they can be handled safely, remove them from the muffin tins and let cool completely on wire racks before frosting. Garnish with crystallized ginger.
In a large bowl, add the cream cheese, butter, vanilla, and ginger. Blend thee ingredients with an electric hand mixer until a creamy consistency is reached, while slowly adding the powdered sugar.