Thoroughly wash the Meyer Lemons and sterilize your quart jar. Any glass lidded jar will do, but I prefer the small mouthed quart jars because the curved top helps keep the lemon wedges submerged in liquid.
Prepare the lemons: slice off both ends of each lemon, being careful to leave some pith. Setting each lemon on one end, slice down as if you are cutting the lemon in half, but stop before cutting all the way through. Repeat crosswise, cutting the lemon into quarters. Again, do not cut all the way through – you want the lemons to open up like a flower, but remain attached at the bottom. Repeat with all the lemons.
Pour enough salt in the bottom of the jar to cover it (about 2 tablespoons). Holding the cut lemons over the mouth of the jar, pour a tablespoon of salt into the open “petals” of the lemon. Close the lemon "petals" back up, and pack the lemons tightly into the jar. Add salt between each layer. You can add the bay leaves and cardamom pods as you go, or slip them in once the jar is full. Press the lemons down, releasing some of the juices. Top with additional lemon juice until covered.
Close the lid tightly and store in a cool, dark place for 3 days. Each day, open the jar to press down the lemons to keep them submerged in liquid, and shake up the contents. After the third day, store the jar of lemons in the fridge. Allow them to cure for 3 weeks in the fridge. Shake it occasionally to redistribute the salt.
When ready to use, remove a lemon from the jar and rinse it with cold water. Cut away and discard the inner flesh and pulp of the lemons – the part you want is the preserved lemon peel. Slice or chop the peel as desired and use in all manner of dishes for a bit of tangy, salty-sweet flavor all year long.