Season the Flat Iron steaks generously with salt and pepper. Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the steaks to the skillet and sear on both sides for about 4-5 minutes, or until they reach your desired level of doneness. Remove the steaks from the skillet and set aside to rest.

In the same skillet, add the remaining tablespoon of olive oil and the halved shallots. Sauté the shallots until they are golden brown, about 5 minutes. Pour in the sherry and scrape up any browned bits from the bottom of the skillet. Add the beef broth and thyme sprigs to the skillet. Bring the mixture to a simmer and reduce heat to low. Cover and let it braise for about 20-25 minutes, or until the shallots are tender.

While the shallots are braising, bring a pot of salted water to a boil. Add the diced turnips and cook until tender, about 15 minutes. Drain the turnips and return them to the pot. Add the heavy cream and prepared horseradish to the turnips and mash until smooth and creamy. Season with salt and pepper to taste.

Remove the shallots from the heat and stir in the butter until melted and incorporated. Slice the rested Flat Iron steaks against the grain. Plate the creamy turnip mixture and top with the sliced steak. Spoon the braised shallots and sauce over the top. Garnish with fresh thyme leaves.