Some corn soups such as tomato and corn, spicy corn and poblano and Chinese corn and crayfish don't require any thickening. However, other soups such as corn and tortilla, corn chowder or corn and cheese absolutely need to be thick and creamy. Soup that's hot thickens as it cools enough to eat. Let the soup simmer a minute or two after you add the thickener, then cool some down to see if you need to add more.
Tapioca flour, also known as tapioca starch, has a slightly sweet taste which goes with the sweet taste of corn. Cornstarch is made from ground corn so you won't notice any change in flavor. White flour works as well. Blend the starch-based thickener with water to make a paste. Then, whisk the paste into the soup. Bring to a simmer for two or three minutes to let the starch do its magic. Another option is to throw in a handful of breadcrumbs. In a few minutes they'll dissolve into the soup and thicken it. Cornmeal is another alternative. Scatter a good pinch into the soup while you whisk. Wait a few minutes and repeat until the soup has thickened enough. Masa harina is made from corn kernels soaked in lime, dried and then ground. It is used to make corn tortillas and tamales. Masa harina has a flavor that's much different from cornmeal and imparts that flavor to the soup.
Mash It Up
Beans go with corn in the garden and in the soup pot. Choose a light-colored bean so the soup's color won't change. Garbanzos, white beans and black-eyed peas all work. Red kidney beans, black beans and pinto beans thicken corn soup but also change its color. Put canned or cooked beans in the blender. Add enough liquid to turn the beans into a paste. Stir into the soup and let it simmer and thicken. Mashed potatoes and instant potatoes do the same job. Add a little at a time so you don't end up with corn pudding.
Cream thickens a soup adding richness and not much flavor of its own. Yogurt does the same thing but does add tanginess. Beaten eggs will thicken corn soup much the way it thickens a sauce. Beat the eggs. Add some of the corn soup to the eggs to temper them, then beat again. Add about a cup of the corn soup and whisk. Whisk the mixture into the corn soup as you bring it back up to a simmer -- don't just dump them into the hot soup or they'll curdle and you'll end up with clumps of scrambled eggs. Combining fat with flour is another thickener. Combine butter with equal amounts of flour until completely blended. Drop bits of the mixture into the soup and whisk. Adding cheese to the soup, thickens it but changes the flavor.
Soup to Nuts
Ground nuts are an option to thicken corn soup but the flavor will be altered as well. Grind the nuts into a paste and add to the hot soup. Nut butters have already done the work of grinding for you. Add peanut butter for a peanut corn soup.