Preheat the oven to 425 degrees F.
Spread the Brussels sprouts out onto a baking sheet and toss with the oil. Roast until beginning to brown, about 20 minutes.
While the sprouts are roasting, whisk together the gochujang, orange juice, shallot and garlic. Toss the lightly browned sprouts with the gochujang mixture and continue roasting until glazed and very tender, about 20 minutes more. While the sprouts are roasting, in a medium mixing bowl or one-gallon resealable bag, combine the soy sauce, sesame oil, vinegar, ginger, garlic, Sriracha and sugar. Add the steak to the sesame mixture and marinate for 20 minutes.
Place a large cast-iron skillet over medium heat with the oil. Cook the steak in the skillet to your desired doneness, about 4 minutes per side for medium. Let the steak rest for 5 minutes before slicing.
When the sprouts are finished, toss them with the butter and season with salt. Serve the sprouts with the sliced steak.