For the Tomato Vierge
½ cup extra-virgin olive oil
Make the tomato vierge: Preheat the oven to 400°F.
Put the cherry tomatoes in a baking dish and sprinkle with the sugar and coriander. Bake just until the tomatoes begin to soften and wilt, about 8 minutes. Remove from the oven and add the olive oil, lemon juice, and balsamic vinegar. Mix well and season with flaky salt. Set aside.
Make the fish: In a large nonstick skillet, heat 1 tablespoon of the canola oil over medium-high heat. Season the fillets on both sides with salt and white pepper, then add half the fillets to the pan, flesh-side down. Sear the fish until golden brown, about 3 minutes, then carefully flip the fillets and add 2 tablespoons of the butter to the pan.
Use a spoon to baste the fish with the butter as it melts. Cook until the fish is no longer opaque and is golden brown on the second side, about 3 minutes. Use a fish spatula to transfer the fillets to a paper towel–lined plate. Wipe the pan clean, then repeat with the remaining fish, olive oil, and butter.
Place a fillet onto each of six plates. Stir the basil into the tomato vierge and spoon some over each piece of fish. Serve with grilled zucchini, if you’d like.