Drain tomatoes, reserving 1/3 cup oil; set aside. In a large skillet, saute sliced onions in 3 Tbsp. reserved oil until softened. Add vinegar. Reduce heat to medium-low; cook, stirring occasionally, until deep golden brown, 30-40 minutes., Meanwhile, chop sun-dried tomatoes and transfer to a large bowl. Add the red onion, seasonings and remaining 7 tsp. of the reserved oil. Crumble beef over mixture and mix lightly but thoroughly. Shape into 16 thin patties. Place 2 tablespoons goat cheese on the center of 8 patties. Top with remaining patties and press edges firmly to seal., Grill burgers, covered, over medium heat until a thermometer reads 160° and juices run clear, 5-7 minutes on each side., Place buns, cut side down, on grill until toasted, 1-2 minutes. Serve burgers on buns with onions and, if desired, mixed greens.