Whisk gochujang, green onions, soy sauce, rice vinegar, garlic, ginger, sesame oil, and sugar. Pour half into a zip-top bag with the steak and chill for 30 minutes or up to overnight. Cover and chill the remaining sauce.
Heat oil in a large skillet over medium-high. Transfer the steak with tongs, leaving marinade in the bag, and cook 5 to 8 minutes per side until well browned. Rest the steak on a cutting board.
Add onion, mushrooms, ramen noodles, ramen seasoning, and the marinade from the steak bag to the skillet. Add water, bring to a simmer, and cook 5 to 7 minutes until the noodles are tender.
Slice the steak thinly across the grain. Add it and the reserved sauce to the skillet, toss to combine, and cook a few minutes until hot. Garnish with green onions and serve.