Bring balsamic vinegar to a boil in a small, heavy saucepan. Reduce heat to medium; cook until reduced to 1/4 cup (about 5 minutes). Remove from heat.
Heat oil in a large nonstick skillet over medium-high heat. Add onion, and sauté 10 minutes or until tender. Sprinkle with 1/4 teaspoon salt; sauté 18 minutes or until onions are golden brown. Remove from heat.
Sprinkle steak with remaining 1/4 teaspoon salt, pepper, and thyme. Place steak on a broiler pan coated with cooking spray; broil 6 minutes on each side or until desired degree of doneness. Cutsteak diagonally across grain into thin slices. Serve steak over onions; drizzle with balsamic glaze.
Wine note: Steak and caramelized onions are fabulous partners for numerous red wines. But the balsamic vinegar glaze presents a bit of a challenge since vinegar can make wine taste sharp. One variety stands up especially well to vinegar: syrah (also known as shiraz). There are many great syrah/shirazes available. Try Geyser Peak Winery's shiraz from California, which is dense and lipsmacking-a steal at $18. -Karen MacNeil