Ilse

Intensity and character. Mild cheesy or tangy is usually fine. Sharp, sour, soapy or crayon-like is rancid. Taste a little off a clean dry spoon, which tells you in about a second. And look for water droplets or a wet layer, because moisture is what gets you there.

A sieve rather than cloth is probably your answer and it is a shelf-life problem rather than a spoilage one. Butter contains butyric acid, which in small amounts is part of what butter tastes like and in larger amounts smells cheesy, sour, or worse. Milk solids left behind push it that way and shorten how long the jar keeps.

Deeply browned solids also smell strongly toasty and savoury, which plenty of people describe as parmesan. Between the two, you have built a cheesy batch on purpose without meaning to.