Fill four sterilized 8-ounce jars 3/4 of the way with mushrooms. Place 1 thyme sprig and some serrano pepper slices on top.

Combine white wine, water, kosher salt, sugar, garlic, peppercorns, coriander seeds, and lemon zest in a small saucepan over medium-low heat. Simmer, stirring occasionally, until sugar dissolves, about 5 minutes. Remove from heat and pour over mushroom mixture in each jar.

Tightly seal each jar and transfer to the refrigerator. Chill until flavors meld, 1 to 2 days.