Trim the woody base off the chicken of the woods mushroom (12.7 oz / 360 g), clean it, and cut it into thin slices. Peel 5 garlic cloves.
Pour 1¾ cups (420 ml) vinegar with at least 5% acidity and 1¼ cups (300 ml) white wine into a large pot, add 2½ tablespoons fine salt, and bring to a boil.
Add the mushroom slices and simmer for 20 minutes. Drop in the garlic during the final 5 minutes.
Strain and discard the cooking liquid. Lay the mushrooms and garlic out on a clean kitchen towel so no pieces touch.
Air-dry for 24 hours, turning everything once. With a dehydrator, dry at 122°F (50°C) for 5 to 6 hours instead.
Sterilize a 24-ounce (710 ml) jar and lid for 10 minutes in boiling water or a 212°F (100°C) oven, then let them dry completely.
Build up the jar in layers of mushrooms, scattering peppercorns and rosemary between them. Place the garlic cloves and 2 bay leaves among the slices.
Pour in about 1½ cups (340 ml) olive oil. Swirl and tap the jar to release trapped air, leave it uncovered for 1 hour, then add more oil until it reaches the rim.
Seal the jar and store it in a cool, dark pantry. Wait at least 1 week before opening, and refrigerate once opened.