If you want to remove the peach skin, here’s how: Bring a pot of water to a boil. Set up an ice bath. Use a serrated knife to cut a shallow ‘X’ on the bottom of each peach. Lower as many as will fit into the boiling water and cook for about 1 minute, until the ‘X’ starts to fray. Transfer to the ice bath and peel—the skin should slip right off. Or, if you don’t mind the fuzz, skip the blanching and peeling and start at step 2.
Combine the anchovies, olive oil, vinegar, and a pinch each of salt and pepper in a bowl. Stir with a fork, mashing in the anchovies, until a creamy dressing forms. Taste and adjust the seasoning if needed. It should be very bright and savory, to counter the sweet fruit.
Thinly slice the peaches (I find the easiest way to do this is to cut out wedges with a paring knife while holding the fruit). Add the peach slices to the dressing and toss gently. Season again to taste, adding more oil or vinegar if needed to fully coat the fruit.
Let sit for about 5 minutes, so the fruit can release some of its juices, then serve.