Start by preparing the marinade. In a large mixing bowl, combine the minced garlic, dark balsamic vinegar, Dijon mustard, 2 tablespoons of olive oil, fresh oregano, kosher salt, and ground black pepper. Whisk the ingredients together until they are well blended.
Place the skirt steak into the marinade, ensuring that it is well coated. Cover the bowl with plastic wrap and let it marinate for at least 30 minutes at room temperature, or up to 2 hours in the refrigerator for a deeper flavor.
While the steak is marinating, preheat your oven to 425°F (220°C). This high temperature will help to create a nice sear on the steak and cook the broccolini to perfection.
Line a baking sheet with aluminum foil for easy cleanup. Drizzle the remaining 2 tablespoons of olive oil onto the sheet and spread it around to coat the surface.
Once the steak has finished marinating, remove it from the bowl and place it on one side of the prepared baking sheet. On the other side, arrange the cut broccolini and rinsed white beans. Drizzle a little olive oil over the broccolini and beans, and sprinkle with additional salt and pepper if desired.
Place the baking sheet in the preheated oven and roast for about 15-20 minutes. If you prefer your steak medium-rare, aim for an internal temperature of 130°F (54°C). For medium, aim for 140°F (60°C). Use a meat thermometer to check the doneness of the steak.
Once cooked to your liking, remove the baking sheet from the oven and let the steak rest for about 5 minutes. This allows the juices to redistribute throughout the meat, ensuring every bite is tender and juicy.
Slice the skirt steak against the grain into thin strips. Serve the steak alongside the roasted broccolini and white beans for a colorful and nutritious meal. Drizzle any remaining pan juices over the top for added flavor.