Combine balsamic and sugar in a small saucepan. Stir over medium heat until sugar dissolves. Simmer for 3 minutes until mixture has thickened slightly. Set aside to cool.
Cut each piece of salmon in half, lengthways. Combine ginger, chilli and olive oil in a ceramic dish. Add salmon, season with salt and pepper and turn to coat. Cover and refrigerate for 5 minutes.
Preheat barbecue on medium-high heat. Barbecue the salmon for 1 minute each side or until cooked to your liking. Transfer to a tray, keep warm.
Increase heat to high, add mushrooms, drizzle with a little balsamic mixture and cook for 2-3 minutes each side until tender.
Arrange rocket on serving plate. Top with two slices of salmon then mushrooms, drizzle with a little more balsamic mixture and serve.