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Recipes for cheese soup, sauce, and dip usually call for heating the liquids first and then adding the cheese, rather than starting with cheese and liquid in a cold pot. In [this queso recipe](https://cafedelites.com/queso/#wprm-recipe-container-67197), milk (with aromatics and seasonings, but I don't think that affects the outcome) are brought to a boil and then the cheese is mixed in. In [this recipe for macaroni and cheese](https://joyfoodsunshine.com/homemade-mac-and-cheese/#wprm-recipe-container-15774), milk and sour cream are heated (but not boiled) and then the cheese is mixed in. I haven't made either of the recipes I linked, but I have in the past made a cheese soup that took the same approach and my (US) grated cheddar melted.
Update: today I made a cheese sauce thus: put some butter, cream cheese, and cream in a pot and heated slowly until it was all liquid, then added seasonings, then stirred in cheese and turned off the heat. The cheese was a mix of Monterey Jack and cheddar. I ended up with a smooth cheese sauce, no cheese clumps.
All recipes I've seen start with grated cheese. If you're cubing or slicing it, try grating it instead.
I do not know how US cheddar compares to cheddar in other countries, and I've not tried this with other cheeses like gouda.

Recipes for cheese soup, sauce, and dip usually call for heating the liquids first and then adding the cheese, rather than starting with cheese and liquid in a cold pot. In [this queso recipe](https://cafedelites.com/queso/#wprm-recipe-container-67197), milk (with aromatics and seasonings, but I don't think that affects the outcome) are brought to a boil and then the cheese is mixed in. In [this recipe for macaroni and cheese](https://joyfoodsunshine.com/homemade-mac-and-cheese/#wprm-recipe-container-15774), milk and sour cream are heated (but not boiled) and then the cheese is mixed in. I haven't made either of the recipes I linked, but I have in the past made a cheese soup that took the same approach and my (US) grated cheddar melted.
All recipes I've seen start with grated cheese. If you're cubing or slicing it, try grating it instead.
I do not know how US cheddar compares to cheddar in other countries, and I've not tried this with other cheeses like gouda.