Cut the halloumi into strips about ¼-inch thick. Cut the strips into smaller pieces, about 1 ½ X 1-inch. Set aside.
Trim, wash and spin dry the arugula and mint or basil. Tear apart the arugula by hand. trim and chop the fresh mint or basil. Hull and halve or quarter the strawberries.
Whisk together all the ingredients for the dressing and set aside. Drizzle the salad with most of the dressing, reserving a tablespoon or two for garnish. Toss gently.
Heat a grill pan over high heat and grill the halloumi pieces until lined with brown grill marks. Turn to grill on the other side. Place the halloumi pieces around the salad. Drizzle with the remaining dressing and serve.