Preheat oven to 350 degrees F.
In a large bowl, whisk together pumpkin, eggs, oil, butter, brown sugar, granulated sugar, and vanilla until smooth.
In a small bowl, whisk together flour, salt, cardamom, cinnamon, baking powder, and baking soda. Add dry mix to wet ingredients and stir until no lumps are found. (You can't overmix because there is no gluten, so it won't get tough.)
Pour batter into a greased or parchment lined 9x9 inch baking pan. Use spoon to spread the batter evenly. Bake for 18 to 20 minutes, until toothpick comes out with a few crumbs. Remove cake from oven and let fully cool on cooling rack.
Meanwhile beat cream cheese and butter until smooth (I use a hand mixer). Add powdered sugar, vanilla, and salt. Beat again until light, smooth, and whipped. Once bars are fully cool, frost and enjoy. Store them covered in the fridge for up to 4 days.