Swai is a white fish that has been popular in Laos, Cambodia and Vietnam for many years, but it has only been readily available in the United States for the last few years. Swai has a mild, slightly sweet flavor and a light, flaky texture that lends itself to baking, as it can sometimes fall apart when grilled. Swai also pairs well with sweet fruit-based sauces, and should be served with a dry white wine like chardonnay or sauvignon blanc.
Take the swai fillets out of the refrigerator 90 minutes before you want to cook them to warm up to room temperature. Keep the fish covered with plastic wrap.
Preheat the oven to 350 degrees Fahrenheit.
Brush the bottom of a baking dish with the melted unsalted butter. The dish should be large enough to hold the swai fillets without overlapping.
Place the swai fillets in the baking dish and brush the tops of the fish with the extra virgin olive oil. Season the fish with sea salt or kosher salt and freshly ground black pepper, to taste.
Bake the swai fillets in the oven for 12 minutes. Do not check the fish fillets during the cooking time.
Check the internal temperature of the thickest swai fillet in the center with an instant-read thermometer. The fish is completely cooked when the internal temperature is 140 degrees Fahrenheit.
Put the fish back in the oven in 5-minute intervals if it is not fully cooked, checking the temperature after each interval.
Transfer the swai fillets to a large serving platter. Top the fillets with chopped fresh flat-leaf parsley. Garnish the plate with the lemon wedges and serve while hot.