Heat the grill or grill pan. Preheat to medium-high. You want it hot enough to sear quickly without turning the peaches mushy.

Prep the peaches. Halve the peaches and remove the pits. Slice each half into thick wedges (about 3–4 wedges per half). Lightly brush with olive oil and season with a pinch of salt.

Toast the nuts. If not already toasted, warm a dry skillet over medium heat. Add nuts and stir until fragrant and lightly golden, 3–4 minutes. Cool, then roughly chop.

Make the vinaigrette. In a small jar, combine 3 tablespoons olive oil, the zest of half a lemon, 1 tablespoon lemon juice, 1 teaspoon Dijon, 1–2 teaspoons honey, a pinch of salt, and a few grinds of pepper. Shake until emulsified. Taste and adjust acidity or sweetness as needed.

Grill the peaches. Place wedges on the hot grill, cut side down. Cook 1–2 minutes per side until grill marks appear and the fruit softens slightly. Don’t overcook; you want them tender, not collapsing.

Dress the greens. Add arugula to a bowl. Drizzle lightly with vinaigrette and toss gently so the leaves are just coated. Save extra dressing for finishing.

Assemble. Divide dressed arugula between two plates. Tear the burrata open and nestle chunks over the greens. Arrange warm peach wedges on top. Sprinkle with chopped nuts and torn basil.

Finish. Spoon a little more vinaigrette over everything. Add a few twists of black pepper and a pinch of flaky salt. For extra shine, drizzle with a thin ribbon of olive oil or a little balsamic glaze.

Serve immediately. This salad shines when the peaches are warm and the burrata is cool and creamy.