For the dressing, whisk together the olive oil, mustard, sugar, buttermilk, lemon juice, and mint. Season to taste with salt and allow to sit at room temperature for at least 20 minutes and up to two hours so that the flavors combine.
For the mahi mahi, preheat a grill using charcoal or gas heat. Place the fillets on the coolest part of the grill and the peach halves over the hot part of the fire. Cover the grill and cook about 15-20 minutes for fillets 1 1/2 inches thick. The fish should be cooked through but only just beginning to flake when gentle pressure is applied. At that point, the peaches will be slightly charred and beginning to soften.
To serve, mix the arugula and onion, toss with two-thirds of the dressing, and season with salt. Divide the salad among 4 plates. Place 2 grilled peach halves next to the salad. Place a piece of mahi mahi on top of the salad and spoon the remaining dressing over it. Serve immediately.