Strip the kale leaves off the tough stems; discard the stems. Place the leaves in a salad spinner and add enough cold water to cover. Swish the leaves to remove any grit, let stand undisturbed for 1 minute to let any dirt sink to the bottom, and then lift out the colander insert. Rinse out the spinner bowl. If the greens are really dirty, repeat. Spin the leaves until dry. Stack a small bunch of leaves on a cutting board, then roll tightly like a sleeping bag. Cut the leaves into ⅛-inch slices and transfer to a large bowl. Repeat with the remaining leaves.
Using a Microplane grater, zest the lemon directly over the greens, then squeeze the juice over the greens, letting it flow through your fingers to catch any seeds. Sprinkle with ¾ teaspoon salt and ¼ teaspoon pepper, then use your hands to massage the kale until it’s coated with the juice, salt and pepper. The leaves should be softened and about two-thirds their original volume. Let sit while you cut the dates and peaches: Quarter the dates lengthwise, then cut into ¼-inch slices crosswise; pit the peaches, then cut into ½-inch chunks.
Toss the dates, peaches and walnut oil with the kale until well-mixed. Season to taste with salt and pepper. Right before serving, top with the pepitas.
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