Brush steak with olive oil, then press into ground peppercorns and sprinkle with salt; set aside.
Melt butter in a large skillet over medium-high heat. Add steaks, and cook to desired degree of doneness, about 4-6 minutes per side for medium-rare. Remove steaks to a plate, tent with foil and keep warm.
Add onion and mushrooms to skillet and saute until onion goes limp, about 3 minutes.
Stir the minced garlic into the skillet, and cook over medium heat until the garlic begins to brown around the edges, about 1 minute.
Pour in the balsamic vinegar, increase heat to medium-high, and simmer until the vinegar has reduced by half, 10-15 minutes.
Thinly slice the flat iron steak across the grain, and arrange on a serving platter. Pour the reduced balsamic glaze over the meat, and sprinkle with chopped parsley to garnish.