This elegant dish is incredibly simple. If your fishmonger doesn’t have smaller grey sole fillets, buy two larger 8- to 10-ounce fillets and halve them crosswise. Slideshow: More Fast Fish Recipes
Season the fish with salt and pepper. In a large skillet, melt 2 tablespoons of the butter with 1 thyme sprig and cook until starting to brown. Add 2 sole fillets and cook over moderately high heat, turning once, until golden brown, about 4 minutes. Transfer to a platter; tent with foil. Repeat with the remaining butter, thyme and fish.
In a medium bowl, toss the fennel fronds with the celery, parsley, cilantro and Thai basil leaves. Drizzle with olive oil, season with salt and pepper and toss to coat.
Transfer the sole to a platter or plates and top with the herb salad. Serve immediately, passing lemon wedges at the table.