Cook noodles in a large saucepan of boiling water following packet directions until tender. Drain and rinse under cold running water.
Make the dressing - combine tamari, mirin, sesame oil, honey, ginger and sesame seeds. Set aside for later.
In a separate bowl combine the extra mirin, vinegar, honey and ginger.
Heat 1 tbs EVOO in a large non-stick frying pan over medium-high heat. Trim visible fat from steak and then season with salt and pepper. Cook (turning the steak at the halfway point) for 5 minutes for medium. Transfer to a plate. Cover and set aside for 5-10 minutes.
Heat 1 tbs EVOO in pan over medium-high heat. Add the radish, carrot and halved brussel sprouts. Season with salt and pepper. Cook, for 5-6 minutes or until golden brown, stirring regularly. Add mirin mixture (mirin, vinegar, honey & ginger). Cook for 2 more minutes or until glazed and sticky, stirring regularly. Add in 1 tsp of sesame seeds.
Thinly slice the beef. Divide the noodles in the bowls and top with honey glazed vegetables and beef. Finish with the dressing and sprinkle the remaining sesame seeds.