Preparation Line large baking sheet with parchment paper. Mix ground beef, chopped sun-dried tomatoes, 2 tablespoons reserved tomato oil, grated onion, dried basil, ground cumin, 1/2 teaspoon salt, and 1/4 teaspoon pepper in large bowl. Form mixture into 8 patties. Transfer patties to prepared baking sheet. Cover with plastic wrap and refrigerate at least 1 hour. (Can be prepared 4 hours ahead. Keep chilled.) Prepare barbecue (medium-high heat). Heat remaining 4 tablespoons reserved tomato oil in heavy large skillet over medium-high heat. Add sliced onions and sauté until soft and starting to brown, about 10 minutes. Add balsamic vinegar. Sprinkle with salt and pepper. Simmer until onions are deep brown, stirring occasionally, about 10 minutes. Remove from heat. (Can be prepared 1 hour ahead. Let stand at room temperature. Wrap in foil and reheat on grill 10 minutes before serving.) Grill burgers until cooked through, about 5 minutes per side. Place 1 burger on bottom half of each bun. Top with onions and bun tops and serve.
Preparation Line large baking sheet with parchment paper. Mix ground beef, chopped sun-dried tomatoes, 2 tablespoons reserved tomato oil, grated onion, dried basil, ground cumin, 1/2 teaspoon salt, and 1/4 teaspoon pepper in large bowl. Form mixture into 8 patties. Transfer patties to prepared baking sheet. Cover with plastic wrap and refrigerate at least 1 hour. (Can be prepared 4 hours ahead. Keep chilled.) Prepare barbecue (medium-high heat). Heat remaining 4 tablespoons reserved tomato oil in heavy large skillet over medium-high heat. Add sliced onions and sauté until soft and starting to brown, about 10 minutes. Add balsamic vinegar. Sprinkle with salt and pepper. Simmer until onions are deep brown, stirring occasionally, about 10 minutes. Remove from heat. (Can be prepared 1 hour ahead. Let stand at room temperature. Wrap in foil and reheat on grill 10 minutes before serving.) Grill burgers until cooked through, about 5 minutes per side. Place 1 burger on bottom half of each bun. Top with onions and bun tops and serve.