Potatoes were not the hardest nightshade for me to give up (peppers were, because I used to LOVE hot sauce), but they were one of the first things I was desparate for which to find a suitable replacement. My mother is Irish in descent, and we had some potato product on the dinner table easily 5 nights a week. Potatoes, and recipes that contain them, are tied in my brain and in my mouth to the feeling of family, home, and comfort.
Potatoes are ubiquitous, used in all kinds of cuisines for everything from making a soup creamy to binding veggie burger ingredients to taking the center stage as a baked potato. If you find yourself missing potatoes, or have a recipe that has potatoes as an ingredient, consider some of the following substitutions.
Each of the following vegetables (almost all of which are roots) is a good potato substitution for different reasons, and for different forms of potato, so mix and match at will.
Sweet Potato: Despite the name, sweet potatoes (also called yams) are not actually related to potatoes. Which is good for those of us who can't eat nightshades! You can bake sweet potatoes, mash them, turn them into fries, and fry them up for hash browns, all like you can with potatoes. There are varieties of white sweet potatoes that are starchier and less sweet than the orange tubers you probably think of when you think of sweet potatoes; those work great as replacements for potatoes, but brown quickly when the raw flesh is exposed to air. Japanese yams are also whitish (with purple skin), starchier, and less sweet than most sweet potatoes.
Taro Root: While taro root can be difficult to come by, and I've never actually seen it organic, most Asian markets have some in stock. They come in two sizes: large, which aren't as sweet, and baby, which are smaller than your fist and a little sweeter. Boiled and mashed, it makes a great substitution for potato. You can also chop it up and include it in soups and stews, but it gets grainy if you overcook it. Taro root is sweeter than a potato, but not as sweet as a sweet potato. Roasting it for chips or fries brings out that sweetness a litle more than boiling it. I have recipes for mashed taro and taro patties here.
Cassava/Yuca/Manioc/Tapioca: These are four names for one root. Cassava doesn't keep long, so if you find it in a store, its skin is likely to be covered in a thick wax. It can be difficult to find, though grocery stores that stock Latin, Caribbean, and African ingredients often have them, because all of those cuisines use cassava. Cassava can be fried, sauteed, baked, boiled, and mashed. Let me tell you, though, overcooking this baby results in a starchy, gluey texture. Tapioca starch, also made from cassava, is a great replacement for potato starch.
Sunchoke/Jerusalem Artichoke: Sunchokes have a bright flavor, and don't ever get as mushy and grainy as potatoes, which can be a real asset in dishes in which you want your potato-like substitute to maintain its shape and struccture. Use them in soups, stews, and "potato" salads. You can also grate them and use them as hash browns, but they cook down a lot. I have a recipe for potato-style sunchoke salad here.
Celeriac: Celeriac, or celery root, has a distinct flavor of its own, but it is a tasty root vegetable in its own right, and you can use it in place of chopped or diced potatoes in soups and roasts--and even as oven fries, as I posted in this entry.
Turnip/Rutabaga: Like celeriac, turnips and rutabagas have distinct flavor, but give a nice, earthy, root-vegetably flavor and texture for use in almost any recipe where you'd use chopped or diced potatoes. I have an entry about what I do with turnips here.
Bread/flour/starch: I know this sounds crazy, but wait: in recipes like blended soups, where potatoes aren't the main focus but are there to make a soup creamy, you can substitute a large piece of bread. Simply remove the crust, then blend the piece of bread in a blender or food processor with a cup of water and/or a cup of the broth, then stir back into the soup. Also, many recipes, like potato pancakes (latkes; I have a recipe here for sweet potato ones), gnocchi, or veggie burgers, call for cooked potatoes. This is because potatoes are very starchy (much more so than sweet potatoes), and the starch in them acts as a binding agent. For each 1 cup cooked potatoes you replace in these recipes, add 2 Tbsp to 1/4 cup flour, depending on desired stiffness. You can add more if your dough (or recipe) doesn't stiffen as much as you'd like, and you can experiment with also adding some cornstarch or other starch (like tapioca).
Finally, as a word of warning to people who are new to avoiding nightshades: potato starch, like paprika and cayenne, is really sneaky, and works its way into all sorts of things. Almost all store-bought gluten-free flours and baked goods contain potato starch, as do all powdered egg substitutes (like Ener-G or Bob's Red Mill), so be careful about eating baked goods whose ingredients you don't know. Other ubiquitous ingredients that can sometimes be potato-derived are maltodextrin and "modified food starch." Both are usually from corn, but be careful. Also remember that some vodkas are distilled from potatoes. Some nightshade-free people can digest potato vodka, others can't--know what you're drinking. Most brands' websites mention whether theirs comes from grain (usually wheat or rye) or potato.