How to Make It
In a mini food processor, combine the parsley with the olive oil, shallot and lemon juice and process to a coarse puree. Season with salt and pepper.
In a shallow bowl, mix the flour with 1 teaspoon of salt and 1/2 teaspoon of pepper. Press 1 tablespoon of the thyme leaves onto the halibut and dredge in the flour, shaking off the excess.
In a large nonstick skillet, melt the butter. When the foam subsides, add the halibut pieces and cook over moderately high heat, turning once, until golden brown and just cooked, about 3 minutes per side. Reduce the heat to moderate if the fish is getting too dark. Transfer the halibut to plates and sprinkle with the remaining 1 teaspoon of thyme leaves. Serve with the parsley sauce.