Pat the flank steak dry with paper towels on both sides and place it in a resealable plastic bag.
Add the olive oil, red wine vinegar, fresh oregano, grated garlic, cumin, paprika, kosher salt, and black pepper to the bag. Seal the bag, massage the marinade mixture all over the steak, and let it marinate for at least 30 minutes or up to overnight.
While the steak is marinating, preheat an outdoor grill or indoor grill pan to medium-high heat.
In a bowl, toss the vegetables with olive oil, balsamic vinegar, grated garlic, kosher salt, and black pepper until evenly coated.
Once the grill is hot, grill the flank steak for 4-5 minutes per side until charred on the outside and medium-rare in the center. Once done, let the steak rest for at least 5 minutes before slicing.
Grill the vegetables for 2-3 minutes per side until charred on the outside.
After the steak has rested, slice it against the grain into thin slices and arrange it on a wide platter along with the grilled vegetables. Garnish with chopped parsley.