Preheat oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners. In a large bowl, combine vegetable oil, granulated sugar, and light brown sugar. Whisk until smooth. Stir in grated carrots and drained crushed pineapple.

In a separate small bowl, whisk 2 large eggs and 2 teaspoons vanilla extract. Add to the wet ingredients and mix until just combined. In a medium bowl, whisk together flour, baking soda, cinnamon, allspice, salt, nutmeg, and ginger. Gradually add dry ingredients to wet ingredients, mixing until just combined. Do not overmix.

Divide batter evenly among prepared muffin cups, filling each about two-thirds full. Bake for 18-22 minutes, or until a skewer inserted into the center comes out clean. Cool in muffin tin for 5-10 minutes, then transfer to a wire rack to cool completely.

While cupcakes cool, prepare the cheesecake topping. Beat 6 ounces of softened cream cheese until smooth. Gradually add granulated sugar and light brown sugar, beating until light and fluffy. Stir in vanilla extract.

Once cupcakes are completely cooled, spoon or pipe the cream cheese topping onto each cupcake. Garnish with chopped nuts or grated carrot if desired. Chill cupcakes in the refrigerator for at least 30 minutes before serving.