Melt 1/2 tablespoon butter in a skillet over medium heat. Add the shallot and cook, stirring occasionally, until just soft, about 3 minutes. Stir in the tomato, vinegar, 1/4 cup water, 1 tablespoon tarragon and 1/4 teaspoon each salt and pepper; bring to a simmer and cook until reduced by half, about 5 minutes. Remove from the heat.
Place the green beans in a large microwave-safe bowl. Drizzle with 1 tablespoon water, cover with plastic wrap and microwave until crisp-tender, about 4 minutes. Season with salt and pepper; keep warm.
Put the cornmeal in a shallow bowl. Dredge the fish in the cornmeal, shaking off the excess. Heat 1/2 tablespoon butter in a large nonstick skillet over medium-high heat. Working in batches, add the fish and cook until golden, turning once, about 5 minutes. (Add more butter between batches, if needed.) Transfer the fish to plates.
Return the sauce to medium heat. Add the half-and-half, bring to a simmer and cook until slightly thickened, about 3 minutes. Stir in the remaining 1 tablespoon tarragon and 1/2 tablespoon butter and season with salt. Serve the fish with the green beans and top with the sauce.
Per serving: Calories 380; Fat 14 g (Saturated 7 g); Cholesterol 164 mg; Sodium 238 mg; Carbohydrate 30 g; Fiber 4 g; Protein 33 g
Photograph by Antonis Achilleos
Recipe courtesy Food Network Magazine