I've been skilling Parrying on RUN and even tried as COR, I'm at 314 and have tried both, Elshena and Montagna, which seem to overlap at this level. I have heard Parrying happens more with Staves, More with Swords, etc. I bought a sword for RUN and popped Montagna, despite getting 2 levels of sword skill and parrying 5-7 times in about 2-3 minutes, not a single parrying skill up.

Do Skill up foods not cover Parrying? Does another food cover it?

EDIT: Forgot to point out while I WAS gaining skill under the effect of food, it was at the exact same rate as without.