Barramundi, delicious and flaky, goes by another name in some circles: "passion fish." That romantic and emotional name is apropos here, for we find the delicate fish paired with the smooth white wine-butter sauce passionately delicious. And maybe the Swiss aren't known for their romance, but the chard that bears their name is mighty tasty with potatoes and parsnips. Serve this meal to your special someone, and see if the passion fish can live up to its name. (It can.)
Peel and cut potato into 1" dice. Trim ends off parsnip and cut into ½" dice. Stem Swiss chard and trim stalks. Cut stems into ½" slices on an angle and coarsely chop leaves. Mince garlic. Pat barramundi dry, and season both sides with ¼ tsp. salt and a pinch of pepper.
Sear the Vegetables
Heat 1 Tbsp. olive oil in a large non-stick pan over medium heat. Add potato to hot pan and cook, stirring often, 5 minutes. Add parsnip and cook until lightly browned all over, 4-6 minutes. Stir in chard stems, ½ tsp. salt, and ¼ tsp. pepper.
Roast the Vegetables
Transfer vegetables to prepared baking sheet and spread into a single layer. Roast 12 minutes. Remove from oven and carefully stir in chard leaves, garlic, and 2 tsp. olive oil. Roast until chard leaves are wilted, 2-4 minutes. Reserve pan; no need to wipe clean.
Cook the Barramundi
Return pan used to sear vegetables to medium-high heat. Add 2 tsp. olive oil and barramundi to hot pan. Cook until golden brown and barramundi reaches a minimum internal temperature of 145 degrees, 3-4 minutes per side. Remove barramundi to plate. Wipe pan clean and reserve.
Make the Beurre Blanc
Return pan used to cook barramundi to medium heat. Add white wine to hot pan and cook until reduced by ¾, 2-4 minutes. Remove pan from burner. Add butter to pan and swirl to incorporate.
Plate the Dish
Place barramundi on a plate and add vegetables next to fish. Spoon beurre blanc next or on top of barramundi.