Put the tomatoes and mushrooms in a roasting tin, drizzle with about 2 tablespoons oil, season to taste with salt and pepper and cook in a preheated oven, 180°C (350°F), Gas Mark 4, for 10 minutes.
Meanwhile, cut the courgettes into batons about 4 x 2 cm (1½ x ¾ inch) and put them in a large bowl with the trimmed asparagus. Drizzle with olive oil and a pinch of salt and pepper. Heat a griddle pan over a high heat and grill the asparagus and courgettes. Transfer the asparagus and courgettes to the oven with the other vegetables and cook for a further 6—8 minutes.
Cut the haloumi into 5 mm (¼ inch) slices. Heat 1 teaspoon olive oil in a large frying pan over a medium heat and cook the cheese slices until golden.
Make the dressing by whisking the oil and vinegar. Stack the vegetables on serving plates, top with slices of cheese, spoon over the dressing and serve.