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Whisk together all the ingredients for the dressing and set aside.
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Place the arugula in individual serving bowls or in one large bowl or shallow serving platter.
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Heat the grill pan to medium.
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In a small bowl, toss the pears with a tablespoon or so of olive oil and place flat-side down in the grill pan. Sear for a few minutes, until deep golden grill marks form and turn onto the rounded side, using tongs. Sear on the other side for a fewminutes until softened but still firm. Remove.
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Lightly oil the grill pan, tilting back and forth so that the oil is distributed evenly over the surface. Place the halloumi slices in the pan. Sear then flip using tongs or a spatula and continue searing the other side until grill marks take shape there, too.
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Drizzle the arugula about two-thirds of the dressing and toss gently. Place the halloumi and pears over the arugula and drizzle with remaining dressing. Serve.