Wipe the mushrooms with a damp cloth to clean them, and trim the stalks so that they are even with the caps. Place mushrooms in a medium saucepan.
Peel the ginger and cut into quarters. Add to the mushrooms, along with the lemon zest, onion, vinegar, salt and peppercorns. Bring the mixture to a boil and simmer for 15-20 minutes, or until mushrooms are tender.
Remove the mushrooms from the cooking liquid with a slotted spoon and pack into sterilized jars. Strain the cooking liquid and bring it back to a boil. Pour hot liquid over the mushrooms until the level of the liquid is 1/2 inch above the mushrooms. Seal the jars and store in the refrigerator.