Pre-heat oven to 350°F.
Grease a 9 x 5-inch loaf pan and line it with a strip of parchment paper that hangs over the two long sides; grease the paper too.
To a large bowl, add the light brown sugar and eggs and whisk vigorously until pale in color, about 2 minutes.
Add the oil, cinnamon, cardamom and salt; whisk until well combined and smooth.
Add the flour, baking powder and baking soda, and whisk, starting slowly to incorporate the flour without spilling it, until well combined and smooth, switching to a rubber spatula if necessary.
Fold in the grated carrots; the batter will be very thick; scrape the batter into the prepared pan and smooth the top.
Tap the pan on the counter a few times to remove any big air bubbles.
Bake the cake until golden and puffed and a tester inserted into the center comes out clean, 50 to 60 minutes.
Set the pan on a rack to cool for 10 minutes.
After 10 minutes, use the parchment paper to lift the cake out of the pan and set on the rack over a baking sheet to cool completely.