Preheat a grill pan or outdoor grill over medium-high heat.
Brush the cut sides of each peach half with a light coat of olive oil.
Place the peaches cut-side down on the hot grill.
Grill for 2–3 minutes or until deep grill marks appear and peaches are lightly softened.
Remove from the heat and let cool slightly before slicing into thick wedges.
Cut the watermelon into even, bite-sized cubes.
Use a vegetable peeler or mandoline to slice the cucumber into thin ribbons.
Lightly toast the sesame seeds in a dry skillet over medium heat for about 1–2 minutes until golden and fragrant.
To make the dressing, add the miso paste, lime juice, honey or maple syrup, grated ginger, olive oil, and rice vinegar to a small jar with a lid.
Close the jar tightly and shake vigorously until the dressing looks smooth and slightly thickened.
In a large serving bowl, add the baby arugula.
Top with watermelon cubes, grilled peach wedges, and cucumber ribbons.
Drizzle the ginger-lime miso dressing over the salad.
Sprinkle the toasted sesame seeds and chopped mint on top.
Toss gently to combine and serve immediately.