How to Make It
Heat 2 tablespoons oil in a large skillet over medium-low. Add onions and 1/8 teaspoon salt; cook 25 minutes or until deep golden brown. Add sugar; cook 2 minutes, stirring occasionally. Stir in vinegar and thyme; cook 3 minutes, stirring frequently. Place onion mixture in a bowl.
Increase heat to medium-high. Add 2 teaspoons oil to pan. Sprinkle steak with remaining 1/4 teaspoon salt and pepper. Add steak to pan; cook 4 minutes on each side for medium-rare or until desired degree of doneness. Place steak on a cutting board; let stand 10 minutes. Cut across the grain into thin slices.
Spread about 1/4 cup onion mixture over each bread slice. Top evenly with steak, arugula, and goat cheese; drizzle evenly with remaining 1 teaspoon olive oil.