• Preheat oven to 350 degrees Fahrenheit/180 degrees Celsius. Prepare a loaf pan by oiling and then flouring it.
• In a large bowl, whisk the flour, baking soda, baking powder, salt and cardamom.
  
• Add the oil, sugar, applesauce and grated carrots to the bowl.
  
• Mix with a spatula until there's no dry flour in the bowl. The batter will be a little thick.
  
• Add the chopped walnuts to the bowl and mix them in.
  
• Scrape all the batter into the prepared loaf pan. Smooth the top with the spatula, if needed.
  
• Bake 50 minutes or until a toothpick inserted in the center of the carrot bread comes out clean.
  
• Cool on a rack about 15 minutes, then slide a knife around the edges to unmold. Place right-side-up on a rack to cool

Make the glaze

• Use a whisk to beat together the cream cheese, butter, powdered sugar and vanilla until a smooth, thick glaze forms. Pour the glaze over the cooled bread and let it set 30 minutes at least before serving.