This is a charade - multiple parts are joined together in sequence to form the answer. Look for words or phrases that can be broken down into smaller components.
Break down 'Mum's getting fish served with one' into parts: 'Mum's' gives you a possessive form, 'fish' needs a specific type, and 'one' appears directly. These three elements combine in order to spell out the cheese.
Answer: MASCARPONE | MA'S (Mum's) + CARP (fish) + ONE = MASCARPONE (type of cheese)