Arrange oven rack in lowest position. Preheat oven to 450 degrees F.
In a medium bowl, combine horseradish, vinegar, lemon juice, syrup, 1/4 tsp salt and 1/4 tsp pepper. Stir grated apples into horseradish mixture. Set aside.
Heat 12" ovenproof skillet on high. Pat steaks dry with paper towels. Sprinkle with 1/2 tsp EACH of salt and pepper. Add 1 Tbs oil to pan and swirl to coat bottom evenly. When oil shimmers and is almost smoking, add steaks.
Cook 2 min. With tongs, lift each steak from pan and put back down on SAME side. Cook 1 minute longer, then turn steaks over. Transfer pan to lowest rack of oven and roast for 4 minutes.
Meanwhile, combine 2 Tbs olive oil and thyme in a small bowl. Baste steak with melted mixture. Roast 2-3 minutes longer for medium-rare, or until desired temperature is reached.
Remove pan from oven and baste again. Transfer steaks to cutting board, cover with foil and let rest 5 minutes.
Slice steaks against the grain at an angle. Spoon steak juices on top and serve with apple relish.