I do that all the time and I hate throwing out the leftover or feeding it to our pigs.
So I've taken to dehydrating the leftover parsley and it works beautifully.
Most dehydrator recipes advise drying all herbs at 95', and for parsley they advise drying for an hour then flipping it over for another hour. I find that doesn't even come close to drying it!
When parsley is dry enough to be stored, it needs to be crumbly. Not dry and brown but crumbly and still green. So I dry my parsley at 125' for 2 hours then I check if it's ready. If not, turn it back on for another 30 minutes and check again.
To prepare parsley for drying, cut the stems off and just dry the leaves.
Here is my parsley cut and on the dehydrator tray ready to go.
This batch took about 2 1/2 hours at 125'
I use my wonderful labeller to label all my dehydrated foods with their name and date of dehydration.