Begin by preparing the Korean-style glaze. Combine the glaze ingredients and simmer gently over low heat for approximately 3 minutes, or until the sugar has dissolved.
Season both sides of the filet mignon generously with salt and pepper. In a large heavy, ovenproof skillet, heat the olive oil over medium-high heat until almost smoking. Place the steaks in the hot pan and cook until well seared on 1 side, about 3 minutes. Turn the steaks over; there should be a nice crust on top. Then transfer the pan to the oven. Roast for 10 to 12 minutes until the steaks are cooked medium-rare (add 4 more minutes for medium). With 1 minute to go, brush steaks with the glaze.
When done remove the steaks and brush again with remaining glaze. Transfer to a platter and cover loosely to let rest for 5 minutes and keep warm.