In a small bowl, whisk together soy sauce, water, sriracha, sesame oil, and brown sugar. Set aside.
Season thinly sliced beef with kosher salt and freshly ground black pepper. Set aside.
Bring a medium pot of water to a boil. When it comes to a boil, add noodles and cook for 2 ½-3 minutes or until barely cooked through. Drain and rinse immediately in cold water. (You can start the next step while the water is coming to a boil.)
While water is heating, heat oil in a large skillet on medium-high heat. When hot, add the beef in a single layer and cook, stirring frequently, until it’s about ¾ done. Reduce heat to medium and add chopped/sliced onion, garlic, and ginger and cook until beef is cooked through and the mixture is fragrant. Whisk the sauce mixture one more time and then drizzle over the beef and onions. Turn heat to low and simmer while the noodles cook.
When the noodles are cooked and the sauce has been added to the pan, add the drained noodles to the pan and toss gently to combine. Divide the noodles and beef among 4 bowls. Sprinkle with sliced cucumbers, chopped green onions, and sesame seeds and drizzle with a little (or a lot, if you want) Gochujang sauce.