Prep the fennel. Trim the stalks, halve the bulb, remove the core, and slice it as thinly as you can. A mandoline makes this easy, but a sharp knife works, too.
Toss the slices in a bowl with a squeeze of lemon to keep them crisp and bright.
Slice the peaches. Cut into thin wedges. If your peaches are very juicy, pat them dry lightly so the salad doesn’t become watery.
Make a quick dressing. In a small bowl, whisk the pesto with olive oil and 1 tablespoon lemon juice. Taste and adjust.
If it’s too thick, add a splash more oil or lemon; if it’s too sharp, whisk in the honey. Season with salt and pepper.
Assemble the base. In a large bowl, toss the arugula (if using) with half of the dressing. Add the fennel and peaches and toss gently so the fruit doesn’t break up.
Add crunch and herbs. Sprinkle in the pistachios and fennel fronds.
Drizzle over more dressing and toss once or twice to coat everything lightly.
Finish and serve. Taste and adjust salt, pepper, and lemon. If you like, add a few shards of Parmesan on top. Serve right away for the best texture.