Place barramundi fillets on a plate. Combine Dill, Garlic and Parsley in a bowl. Brush herb mixture over one side of fish.
Heat olive oil in a large frying pan. Cook fish herb side down for 2 minutes. Turn, cook for 2 to 3 minutes or until just cooked through.
Meanwhile, boil or steam broccolini, asparagus, green beans and red capsicum. Toss vegetables in extra virgin olive oil and lemon juice. Season with salt and pepper.
Divide vegetables among serving plates. Top with fish. Serve with lime or lemon wedges.