Heat oil in heavy large skillet over mediumhigh heat. Add onions; sprinkle with salt and cook until beginning to brown, stirring often, about 8 minutes. Reduce heat to medium-low. Stir in vinegar and sugar; cook until onions are browned, stirring often, about 15 minutes. Transfer caramelized onions to bowl; reserve skillet.
Meanwhile, cook pasta in large pot of boiling salted water until tender but still firm to bite, stirring occasionally. Drain.
Add wine to reserved skillet. Boil until reduced to 1/2 cup, 3 minutes. Add pasta, onions, broth, and next 4 ingredients. Season with salt and pepper. Stir over medium heat to warm through, about 3 minutes.
Divide spinach among plates. Spoon pasta over spinach. Top with crumbled goat cheese.