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Cut eggplants into 1/2 inch slices. Place on a wire rack, sprinkle with salt and leave for 30 minutes. Rinse and pat dry with paper towels.
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Cut the sweet potatoes into 1/4 inch slices, and the zucchini into 1/2 inch slices lengthwise.
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Quarter the peppers, remove seeds and membranes and chargrill skin-side-down, until the skin blackens and blisters. Place in a plastic bag and leave to cool. Peel away the skin.
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Brush the eggplant, sweet potato, zucchini and mushrooms with oil. Barbecue in batches until lightly browned and cooked through.
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Combine the dressing ingredients in a food processor and process until smooth.
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Mix the vegetables with the dressing. Allow to cool, then cover and refrigerate until ready to use. Return to room temperature before serving.