Mix together 4 tablespoons of the oil, the lemon juice, sugar and parsley in a small bowl. Season with salt and pepper. Set aside.
Pat the cheese slices dry on kitchen paper. Brush the asparagus with the remaining oil and a little seasoning. Place the asparagus on the upper rack of the halogen oven.
Set the temperature to 200°C (392°F) and cook for 5 minutes. Transfer to the lower rack to keep warm. Place the haloumi slices on the upper rack and cook for a couple of minutes on each side. (You will need to cook the cheese in batches.)
Arrange the asparagus and haloumi on serving plates and scatter with the capers. Lightly whisk the dressing and drizzle over the salad. Serve with lemon wedges and grainy bread.