Preheat the oven to 350F. Put the artichoke hearts in a deep sided pot. Cover with cold water and add a bit of salt and a few drops of lemon juice. Bring to a boil and then simmer for 5 minutes. Drain well.
Transfer the drained artichokes to a deep baking dish and add the tomatoes, some thyme (reserve a few sprigs for the fish) and salt. Top with the cultured butter.
Cover the dish and roast for approximately 20 minutes. Increase the heat to 400F.
Heat the clarified butter in a large nonstick skillet over medium-high heat. Quickly sear the cod, about 1 minute per side.
Transfer the fish to a nonstick baking dish and pour over the remaining butter and pan juices from the skillet; season with salt and pepper. Top with the remaining few sprigs of thyme.
Roast in oven for 10 minutes.
Serve the fish with the tomato and artichoke confit. Top with a web of chili threads.