Preheat a grill to medium high. Soak the onion in a bowl of cold water. Whisk the ginger, sugar, olive oil and 1/4 teaspoon salt in a small bowl until the sugar is dissolved.
Season the pork with salt and pepper and rub with 1 tablespoon of the ginger oil. Lightly brush the grill grates with olive oil. Grill the pork, turning as needed, until well marked and a thermometer inserted into the center registers 145 degrees F, 20 to 25 minutes. Transfer to a cutting board and let rest, 5 minutes.
Meanwhile, thinly slice the melon, then cut into 2-inch pieces. Drain the onion and toss with the melon, 1 tablespoon of the ginger oil, the lime juice, mint, and salt and pepper to taste in a large bowl. Sprinkle with the cashews.
Cut each pork tenderloin into 8 pieces and divide among plates. Drizzle with the remaining ginger oil and serve with the melon salad.
Photograph by Antonis Achilleos
Courtesy of Food Network Magazine