Parsley is one of the herbs we use most often in our cooking, and I'm always trying to make sure we have enough of it available (in which I don't always succeed!). I have very little of it in the garden at present, so I have recently been sowing some more.
I sow about 15 or 20 seeds in a 5- or 6-inch pot, using moist general-purpose compost. The seeds are then covered with a thin layer of dry compost, and the pot is placed inside a clear plastic bag.
The bag serves to increase humidity, which aids germination. Germination can be quite slow with Parsley, sometimes as long as 21 days, but a bit of gentle warmth (e.g. from heated propagator) helps speed things up. Mine have been under the Growlights, which are on for 12 hours a day but provide very little heat. Nevertheless the most recent batch germinated in 8 days.
Soon after germination I remove the bag, because excessive humidity at this stage can encourage Damping Off, and other fungal diseases.
Once the seedlings are about a week old they get moved out from under the lights to a windowsill. I hesitate to say "a sunny windowsill", because at this time of year sunshine is a precious and rare commodity, but at least the seedlings get natural light.
Parsley is fairly cold-tolerant, but if the weather is, or is likely to be, frosty, I give the transplants the protection of a cloche. Later plantings of course won't need this.
I now have three such batches of Parsley on the go, about three weeks apart, so hopefully that will be enough for the time being. My only batch that was sown last year was ravaged by birds and is only just beginning to recover.