Heat oil in a large nonstick saucepan over medium-high heat. Add onion, bell peppers and minced thyme; saute 8 minutes. Stir in vermouth, 1/4 teaspoon salt and 1/8 teaspoon pepper. Lower heat and continue cooking 8 minutes more. Cover and set aside.

Meanwhile, pat steak dry and season both sides with remaining salt and pepper. Heat a large grill pan or nonstick skillet over medium heat; add steak and cook 4 minutes. Flip steak and cook 3 to 4 minutes more for medium rare. Transfer to a cutting board and let rest 5 minutes; cut across the grain into thin slices.

Divide onion-and-pepper mixture among four dinner plates and top each with steak slices. Sprinkle with goat cheese and garnish with a thyme sprig.