Fill a plastic freezer bag with a 3-inch layer of loosely-packed moist vermiculite.
Nestle the seed in the surface of the vermiculite so that it is just buried.
Close the bag and place it in a warm area in the greenhouse with consistent temperatures of 70 degrees Fahrenheit or above and is protected from direct sunlight.
Check on the bag once a week to make sure that the vermiculite is moist. If not, spray it with enough water to moisten it but not enough to pool water in the bottom of the bag. Also check on the seed for root growth by gently moving aside the vermiculite beneath the seed with a toothpick. Once a thin, white root emerges and grows to 1 inch in length, move onto the next step.
Cold-stratify the seed to mimic low winter temperatures. If the greenhouse is unheated and temperatures will fall and stabilize around 40 degrees Fahrenheit, put the bag there. If the greenhouse is heated or temperatures will fall far below 40 degrees in the winter, move the bag to your refrigerator's crisper drawer for the winter. Check on it weekly as noted in the instructions for Step 4. But this time, in addition to monitoring moisture levels, you are looking for shoot growth. Once a shoot emerges from the top of the peony seed, proceed to Step 6. If a shoot has not emerged after 12 weeks, move onto Step 6 regardless.
Fill a small pot to within 1/4-inch of its lip with a sterilized commercial potting soil.
Water the mixture until water drains out of the drainage holes in the pot and into the tray beneath it. Empty the pot's tray of standing water after 15 minutes.
Clear a hole in the center of the pot that is as deep as the seed's root. Plant the seed so that the root is below the soil surface and the shoot is above it.
Move the pot to a sunny spot in the greenhouse. Water to keep the soil moist, following the watering steps described in Step 7. Once the fernleaf puts on new growth for the season, only water when the top third of the soil is dry.
Fertilize your fernleaf peony's soil with a balanced liquid houseplant fertilizer once every two weeks. Follow the label's instructions for application amounts. Water your peony after each fertilizer application.
Move the pot to an unheated area, during the winter months until spring, once your fernleaf peony starts to drop its foliage in late summer as it needs cool temperatures at this time.