In a small bowl, whisk together soy sauce, olive oil, vinegar, honey, ginger, and garlic powder. Place flank steak in a large Ziplock freezer bag. Pour the marinade into the bag and toss to coat. Seal the bag and refrigerate for 30 minutes (or up to 24 hours).
Line a large, rimmed baking sheet with aluminum foil and set aside.
Place top oven rack 6 inches from heat. Preheat oven to 450°F (230C). Spread potatoes on the prepared baking sheet. Drizzle potatoes with butter, remaining 1 tablespoon olive oil, ¼ teaspoon salt, and a pinch of black pepper. Toss to coat.
Bake potatoes for about 15 minutes. Stir potatoes and move them to the outer edges of the pan. Place broccolini in the middle of the pan. Place steak on top of the broccolini and discard the remaining marinade in the bag.
Change oven setting to BROIL. Return pan to the oven for 6 minutes. Turn steak, stir vegetables, and broil 6 more minutes (or until it reaches desired doneness).
Remove from oven, allow steak to rest 5 minutes. Slice steak against the grain, and serve with broccolini and potatoes.