Let them go to seed. You can't usually fool Mother Nature by clipping off the flowers and hoping for more growth. Let it seed and self-sow for a nice little parsley patch.

FYI - parsley is a biennial which means it dies in the second year after setting its seed.

FataMorgana

Also, there are some very valuable tiny wasps and bees that need this type of tiny flowered umbel to feed. Allowing parsley and dill to go to seed is a good thing to do.

Also, sow again for this year. With the biennial--if you sow two years, then you'll have one set that is good for leaf, while the other is seeding for the next years' harvest.