Season both sides of a small piece of flank steak with salt and pepper. Heat a pan with some oil until just smoking. Add the steak and sear for about 3-4 minutes per side, 125ºF in the thickest part for rare, or 130ºF for medium rare. Transfer to a cutting board, lightly tent with foil, and let rest for 10 minutes, to allow the juices redistribute.
Meanwhile, get all your garnishes ready and bring a pot of water (about 4 cups) to a boil. Slice the rested steak thinly against the grain, and keep warm with the foil.
Boil both packs of noodles, along with both of the vegetable packets for about 2-3 minutes, or until al dente. You want them to remain undercooked because the noodles will be cooked more in the sauce later.
Dump the noodles in a strainer set over a large bowl. Reserve the cooking water, and fish out about 1 cup of it.
Add the noodles back to the pot. Add the whole packet of the Chapaghetti seasoning packet and about 3/4 of the Neoguri seasoning packet, along with the reserved 1 cup of water. Stir together over medium heat until most of the sauce is absorbed. Feel free to add a little more water if it gets too dry. Divide between two bowls, top with the sliced steak, julienned cucumber, sliced chili pepper, scallions, and sesame seeds. Serve with a side of danmuji (pickled radish).