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¼ cup all purpose flour
2 teaspoons finely grated lemon peel
1 teaspoon coarse kosher salt
½ teaspoon ground white pepper plus additional for seasoning
3 tablespoons olive oil, divided
12 ounces petrale sole fillets
¾ cup thinly sliced shallots
6 ounces brussels sprouts, trimmed and thinly sliced lengthwise
1 cup vegetable broth
1 tablespoon unsalted butter
1 teaspoon chopped fresh Italian parsley
Combine flour, lemon peel, coarse salt, and ½ teaspoon white pepper in shallow bowl. Heat 1 tablespoon olive oil in each of 2 large skillets over medium heat.
Coat fish in flour mixture and shake off excess. Add fish to skillets and cook until opaque and golden brown, 1 to 2 minutes per side. Remove from heat and season to taste with salt. Cover loosely with foil and set aside.
Wipe out 1 skillet. Add remaining 1 tablespoon olive oil and heat over medium heat. Add shallots and sauté until almost translucent, about 2 minutes. Add brussels sprouts and broth. Increase heat to medium-high and cook, stirring occasionally, until brussels sprouts are tender and liquid is almost completely absorbed, about 8 minutes. Remove from heat. Stir in butter. Season to taste with salt and white pepper.
Spoon brussels sprouts onto plates. Top with fish, sprinkle with chopped parsley, and serve.