When dairy products are heated, they sometimes separate or curdle in response to high heat. The milk fats clump together, forming a rubbery mass, while leaving a thin, unappetizing liquid. Patience and low heat are your friends anytime you use milk in a sauce or soup. The higher the fat content of the milk, the less likely it is to curdle. Some recipes call for thickening the soup with a roux made of flour or cornstarch, which reduces the likelihood of curdling, as well.
Simmer the potatoes in salted water or broth, rather than milk, until they're completely tender. If you simmer the potatoes in milk, the milk may curdle. Additionally, broth or salted water adds more flavor to the potatoes than milk would.
Drain some of the water off and add the milk, grated cheese and seasonings. It's best to use whole milk or even half and half for some of the milk. Adding milk at the last minute reduces the chances of it separating.
Heat the soup over medium heat until it is warm, but not piping hot. Do not allow it to boil, which can cause the milk to curdle.
Start With a Roux
Simmer the potatoes in broth or salted water until they're tender. Drain some of the water or broth if you like.
Melt butter in a large saucepan. Saute minced onions in the butter, if you like. Stir in a bit of flour and cook it over medium heat for a minute or two, whisking constantly, until it becomes golden. This cooking process is important to remove any raw flour taste from the soup. You can control the thickness of the soup by the amount of flour you add. Add more flour for a thicker soup.
Pour warm milk slowly into the roux, whisking constantly. Continue whisking until the mixture simmers and thickens slightly, but don't allow it to boil. The flour stabilizes the milk, making it less likely to curdle. It also creates a thick, satisfying soup.
Add the potatoes, broth, grated cheese and seasonings. Heat just until the cheese melts.