Marinate the steak: Trim any large patches of fat from the surface. If necessary, cut the steak crosswise into pieces 8 to 10 inches long. In a 9x13-inch baking dish (or similar), whisk 1/2 cup of the oil, the lemon juice, mustard, lemon zest, honey, pepper flakes, garlic, 1-1/2 tsp. salt, and 1/4 tsp. pepper. Arrange the steak in the dish and turn to coat with the marinade. Cover with plastic and refrigerate for at least 2 hours but preferably overnight.
Make the pickle: In a medium saucepan, stir together the oil, cider vinegar, honey, sherry vinegar, coriander, 1-1/2 tsp. salt, and 1/4 tsp. pepper. Bring to a simmer over medium-high heat. Add the radishes, carrot, onion, and jalapeño and toss gently to coat. Reduce the heat to medium low and cook, stirring occasionally, until the onions are wilted and the radishes are no longer crunchy but are still firm, 4 to 5 minutes. Give it one final stir and remove from the heat. Set aside, uncovered, while you cook the steak.
Cook the steak: Remove the steak from the marinade and pat dry with paper towels. Season on both sides with 1/2 tsp. salt and a few grinds of pepper. Heat 1 Tbs. of the remaining oil in a large skillet over medium-high heat. Add half of the steak to the hot skillet in a single layer and cook, flipping once, until deeply browned on both sides and cooked to your liking—medium rare will take 5 to 7 minutes total. Transfer the steak to a carving board and set aside. Wipe out the skillet with a paper towel, heat the remaining 1 Tbs. oil, and cook the remaining steak as above.
Let the steaks rest for at least 5 minutes; then slice thinly across the grain and transfer to a large platter. Pour any accumulated juices over the steaks, top with the warm radish pickle, and serve.
The steak can be marinated and the pickle prepared up to 1 day ahead. Refrigerate both, and reheat the pickle before serving.