Poke three to four drainage holes in the bottom of the cup with an ice pick or the tip of a pair of scissors. Soak the parsley seeds in a cup of warm water for 24 hours before planting to reduce the germination time.
Fill the planting cups three-quarters full with peat moss. Remove four to five parsley seeds from the water bath and pPress each seed 1/8 inch deep into the peat moss, spaced at least a half-inch apart. Pat the soil over the top.
Spritz the peat moss with just enough water to dampen. Cover the cup with a piece of plastic film and wrap a rubber band around the cup to secure it.
Set the cup on a stable surface, such as your windowsill, where it will receive bright, indirect sunlight. Lift the plastic every few days and press your finger into the peat moss to ensure that it is moist. If not, give it a few spritzes of water with the spray bottle. Replace the plastic.
Remove the plastic wrap from the cup when you see parsley shoots breaking through the soil. New parsley plants look like blades of grass when the seeds first germinate. Germination should take three to six weeks.
Provide the parsley with moist peat moss and bright, indirect sunlight as it grows. Weed out the weakest plants when they develop their second leaves, leaving behind a single parsley plant in the cup to grow.