While the grill heats, prepare all your components so assembly is seamless. In a small jar with a tight lid, combine the balsamic vinegar, Dijon mustard, honey, lemon zest, and sea salt. Shake vigorously for 30 seconds until the vinegar and honey are fully incorporated, then slowly add the extra virgin olive oil while shaking to create an emulsified dressing. I like to make the vinaigrette first so the flavors have time to marry while you're grilling. Place the arugula in a large bowl, tear the basil leaves into bite-sized pieces, roughly chop the walnuts, and tear the prosciutto into bite-sized pieces. Have the crumbled goat cheese ready as well.
Heat your grill to medium-high heat (around 400°F if using a gas grill). While it preheats, brush the cut sides of the halved peaches with the 1 tablespoon of olive oil. Once the grill is hot, place the peaches cut-side down on the grill grates. Cook for 2-3 minutes until you see caramelized grill marks and the peaches soften slightly—you want them to have color but still hold their shape. Remove them from the grill and let them cool on a cutting board for a few minutes, then slice each half into 3-4 wedges.
Pour the vinaigrette from Step 1 over the arugula in the bowl and toss gently but thoroughly to coat all the greens. Divide the dressed arugula among your serving plates, creating a bed for the remaining components. Top each plate with grilled peach slices, then scatter the crumbled goat cheese, toasted walnuts, torn basil, and prosciutto pieces evenly over the greens. I find that layering the components this way—greens first, then peaches and cheese—keeps everything from getting too compressed. Finish with a light sprinkle of flaky sea salt and a crack of freshly ground black pepper.