Preheat oven to 350 degrees F. Line a muffin tin with 12cupcake liners. Peel and shred 2 parsnips. You can shred them by hand or use a food processor. Measure out the shredded parsnips into 2 cups and set aside. Ina stand mixer or a large bowl, combine oil, brown sugar, salt, cardamom, and cinnamon. Whisk in eggs, vanilla, flour, and baking powder. Fold in parsnips last. Scoop batter evenly among 12 cupcake liners. Bake cupcakes for 20-22minutes, or until a toothpick inserted comes out clean. Cool cupcakes at room temperature for about 30 minutes.
Prepare the cranberry jam by heating all ingredients in a small sauce pot. Cook for about 8-10 minutes on medium high until cranberry appears thick like jam, stirring every couple of minutes. Transfer to a food processor and process for about 30 seconds. You want the jam to be smoother, but still a little chunky. Cool jam down at room temperature, about 20 minutes, and then transfer to a piping bag.
Make the cardamom cream cheese frosting by combining cream cheese and butter in a stand mixer fitted with a paddle attachment. Paddle together until smooth, scraping down the sides as needed. Add in powdered sugar, vanilla, cardamom, and cinnamon, and paddle until smooth. Transfer frosting to a piping bag.
To assemble, pipe cardamom cream cheese frosting on each cupcake. Top the frosting with a little cranberry jam. Top cupcakes with some toasted pecans. Enjoy!