This method of preserving them highlights how meaty certain mushrooms can be, and the marinade is a perfect blend of Southern Italian flavors: lemon, chile, olive oil, oregano. I have found that boletes are the best for this: porcini, birch boletes, leccinum species and the like. But any other meaty mushroom works. For store-bought, use cremini, shiitake or king trumpets. You don't need any special equipment to make these mushrooms, but you need time. It takes a day to make them -- or at least a couple hours if you have a dehydrator. But the time spent is more than worth it.
Cut the mushrooms into reasonable pieces. With small mushrooms, like a button mushroom, you need only cut them in half, and you can leave the smaller ones whole. With large chanterelles and porcini, cut them into 1/2 inch thick slices. They will shrink a lot in this process, and they will be pliable, so they can be a little larger than you'd think they ought to be.
Salt them well. Lay down a layer of salt on a sheet tray and place the mushrooms on it. If the mushroom has a flat side, i.e., a button mushroom sliced in half, lay the flat side down against the salt. Sprinkle a heavy layer of salt over the tops of all the mushrooms.
Let this stand at room temperature for 1 to 2 hours. You will notice a lot of water coming out of the mushrooms. This is good. Note that I have left the "sponge" on the porcini in the pictures. I no longer do this because the sponge gets really slimy and icky in this process, and tends to stick to everything. Better to remove the sponge and dry it. It makes great porcini powder.
Put the mushrooms between paper towels and gently squeeze them a bit to remove a little more water.
Boil them in the vinegar for five minutes; you might need more vinegar than a quart, but it should get you started. The mushrooms will want to float. Use tongs or something to submerge them as much as you can. Fish out the mushrooms and put them between paper towels again and gently squeeze them to remove some of the vinegar.
Lay the mushrooms on a clean cloth to dry. Let them air dry until they are no longer damp, but still pliable. Don't let them dry out into leather. Turn the mushrooms once or twice during this time. This will take between 12 to 24 hours, depending on how dry it is in your house and how much air circulation you have going. You can also use a dehydrator to speed up the process, but keep an eye on it: Mushrooms can go from perfect to leather in a hurry if you're not careful!
Add the seasonings. Put the oil, lemon zest, oregano and chile in a bowl and toss the mushrooms in them. Pack this into glass jars. Use a chopstick or some other kind of clean stick to poke around the jar -- you want to find and remove as many air bubbles as possible. Make sure the mushrooms are submerged in the oil. Refrigerate and wait at least a week before eating. These mushrooms will keep in the fridge for 6 months.