To thicken leek and potato soup, add in cooked or mashed potatoes, cooked carrots, or cooked rice, then blend. Another way is to add 1 tablespoon of rice flour or to grate 1-3 raw potatoes to the hot soup, stir then cover, and allow to sit for a few minutes before blending. Alternatively, make a slurry by combining one tablespoon of cornstarch with two tablespoons of water. Grain-free alternatives to thicken up leek and potato soups include cassava flour and tapioca flour. Simply make a slurry in a 1:2 flour to cold-water ratio. Use one tablespoon of almond flour combined with half a teaspoon of xanthan gum or low-carb approved gelatine for low carb.