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 saut 10 minutes or until tender.
Sprinkle with 1/4 teaspoon salt; saut 18 minutes or until onions are golden brown.
Remove from heat.
Preheat broiler.
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 $ -Karen MacNeil