Place the barramundi fillets in a large, deep casserole dish or container.
Whisk together the brown sugar, salt, onion powder, garlic powder, bay leaves and water until the sugar and salt have fully dissolved. Pour the mixture over the fish, cover and refrigerate for 4 hours.
Remove the fillets from the brine and rinse under cold water, then pat very dry. Place the fillets on a rack and refrigerate, uncovered, for about 3-4 hours until the flesh feels tacky.
Prepare a smoker with the wood chips and lightly oil the racks. Place the fillets on the racks and smoke at about 200° F until the flesh reaches an internal temperature of 145° F (about two hours, give or take). Remove from the smoker and cool to room temperature.
In a large salad bowl, whisk together the shallot, lemon juice and olive oil with salt and pepper. Use a vegetable peeler to shave the carrot and asparagus spears into long, thin strips. Use a mandolin slicer to shave the beet and radishes into paper thin rounds. Add the shaved vegetables to the bowl along with the sugar snap peas, arugula, chives and parsley. Toss everything to coat in the dressing, then arrange on a platter.
Pull pieces of the smoked fish away from the skin and arrange on top of the salad. Serve immediately.
Notes: Use the freshest, most colorful spring vegetables that you can find. Look for different colored carrots, watermelon radishes, golden and chioggia beets.