Preheat oven to 350 F. Line a muffin tin with 12 deep cupcake papers.
In a bowl, beat together vegetable oil & sugar; add eggs & grated zucchini & beat again.
In another bowl, whisk together flour, cardamom, baking soda, baking powder & salt.
Add flour mixture alternately with milk then stir in lime zest. Divide batter between the 12 cupcake liners.
Bake for 18-20 minutes (until a skewer comes out clean).
Remove from oven, leave in tin for 10 minutes then transfer to a wire rack to cool completely.
Frosting
In a small bowl, beat cream cheese & butter until light & fluffy. While mixing on low, slowly add powdered sugar & lime juice & beat again until fully combined.
When cupcakes are cooled completely, pipe a rosette on each cupcake & sprinkle with lime zest.