The closest comparison I can think of is baby food, which is indeed restricted. According to IATA TravelCentre:
The International Civil Aviation Organisation, the UN’s aviation
standard-setting body, has defined guidelines that more and more
governments are adopting. The current restrictions for liquids,
aerosols and gels from ICAO and in effect in most many countries are
that they must be in containers 100ml or equivalent, placed in a
transparent resealable plastic bag with max capacity 1-litre. At
screening, plastic bags should be presented apart from other carry on
items.
UK's DirectGov website further elaborates that 'liquids' are:
- all drinks, including water, soup and syrups
- cosmetics and toiletries, including creams, lotions, oils,
perfumes, mascara and lipsticks
- sprays, including shaving foam, hairspray and spray deodorants
pastes, including toothpaste
- gels, including hair and shower gel
- contact lens solution
- any other solutions and items of similar consistency
Based on the final point in the list, it does appear that airport security might have some ground for preventing carriage of, in this case, mozarella cheese if has milky fluid in the same container.