Heat a gas grill to medium-high or the coals in a charcoal grill to medium-hot.
In a small bowl, whisk together vinegar, oil, brown sugar, thyme, oregano and 1/8 teaspoon of the salt.
Cut beef in a circular motion so it becomes a long flat strip of steak 1/2 to 3/4 inch thick. Pound slightly.
Lightly coat grill rack with oil or nonstick cooking spray. Brush sweet potato slices with balsamic mixture and season with 1/4 teaspoon of the remaining salt and 1/8 teaspoon of the pepper. Grill for 6 minutes per side or until fork-tender. Meanwhile, brush beef with remaining balsamic mixture and season with remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Grill 2 minutes per side for medium-rare.
Slice meat into 1/2-inch slices and serve with sweet potatoes.