In a small bowl whisk together gochujang, green onions, soy sauce, rice vinegar, garlic, ginger, sesame oil, and sugar. Pour half of mixture into a large ziplock bag. Add steak to bag, seal, and chill for 30 minutes or up to overnight. Cover remaining sauce and chill until ready to use.
Drizzle oil into a large pan or skillet and bring to medium-high heat. Use tongs to transfer steak from bag to pan (keep marinade in the bag) and cook for 5-8 minutes on each side until well-browned on the outside. Transfer steak to a large cutting board and allow to rest while you move on to the next step.
Add onions, mushrooms, ramen noodles, ramen seasoning, and beef marinade from the bag to the pan. Pour water over the top and bring to a simmer. Allow to cook for 5-7 minutes until noodles are tender and cooked through.
Thinly slice steak across the grain. Add steak strips and reserved sauce to the pan and stir everything to combine. Cook for a few minutes just until steak is hot throughout, garnish with green onions if desired and serve immediately.