How to Make It
Cut top and bottom from watermelon. Slice remaining watermelon into 1-inch-thick vertical slabs, leaving outer peel and rind intact. Place watermelon slabs and halloumi slices on a rimmed baking sheet.
Preheat a gas grill to high (450°F to 500°F). While grill heats, stir together 3 tablespoons of the lime juice, 2 tablespoons of the olive oil, 1 tablespoon of the chopped ginger, and ½ teaspoon of the salt in a small bowl. Pour mixture over watermelon and cheese, turning each piece to coat evenly in the marinade. Chill, uncovered, for 30 minutes.
Meanwhile, in the same small bowl, stir together shallots, honey, and remaining ¼ cup lime juice, ¼ cup olive oil, 1 tablespoon ginger, and ½ teaspoon salt until combined. Let stand at room temperature until ready to use.
Place watermelon on oiled grill grate and grill, uncovered, turning once, until grill marks appear and watermelon is slightly tender, 2 to 3 minutes per side. Transfer watermelon to a cutting board. Place halloumi on grate and grill, uncovered, turning once, until grill marks appear and cheese is slightly softened, about 1 minute per side. Remove from grill and cool on wire rack, about 5 minutes.
Arrange arugula on a large platter. Cut 2 watermelon slabs into wedges (leaving rind intact) and slice halloumi into cubes. Arrange watermelon wedges and halloumi over arugula, and spoon ¼ cup of the vinaigrette over top. Sprinkle with chopped pistachios. Cut remaining watermelon slabs into wedges. Serve salad with remaining watermelon wedges and vinaigrette.