Combine potatoes, corn, onion, butter, beef base, salt, red pepper flakes, and black pepper in a saucepan. Pour enough water over the mixture to cover by 2 inches.
Bring the soup to a boil, reduce heat to medium-low, and simmer until the potatoes are soft, about 20 minutes.
Pour soup into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth.