With their flat bottoms, white donut peaches are easier to serve and eat than rounded ones. Lemon verbena is a fragrant herb that can be found at many farmers' markets in midsummer.
Bring wine, sugar, lemon zest, lemon verbena, and water to a simmer in a medium saucepan over high heat. Carefully add peaches, and reduce heat to medium. Gently simmer until tender all the way to the pit when pierced with a skewer or a sharp knife, 20 to 25 minutes.
Using a slotted spoon, transfer peaches to a plate. Let cool slightly. When cool enough to handle, peel off skin.
Meanwhile, return poaching liquid to a simmer, and cook until reduced by about three-quarters, about 20 minutes. Pour through a sieve, and discard zest and leaves. (You should have about 1 cup syrup.) Let cool for 10 minutes.
Refrigerate single layers of peaches and the syrup in separate airtight containers until cold, at least 30 minutes (or overnight). To serve, place a peach on a serving plate and spoon about 3 tablespoons syrup around each peach. Garnish with lemon verbena if desired.