Melt 3 tablespoons butter in heavy large skillet over medium heat. Add onions, sugar and thyme. Season with salt and pepper. Cook until onions are tender and golden brown, stirring frequently, about 35 minutes. Transfer 1/2 cup onions to blender; transfer remaining onions to bowl. Add broth to same skillet and bring to boil, scraping up any browned bits. Add broth and 1/2 cup cheese to blender. Puree until smooth.
Melt 1 tablespoon butter in heavy large skillet over medium-high heat. Season veal with salt and pepper. Add veal to skillet and cook to desired doneness, about 2 minutes per side for medium-rare. Transfer veal to plates; keep warm.
Add vinegar to skillet; bring to boil, scraping up any browned bits. Add sauce to skillet and cook until heated through. Whisk in remaining 1 tablespoon butter. Season with salt and pepper.
Meanwhile, combine currants and reserved onions in heavy small saucepan and cook over medium-low heat until heated through.
Spoon sauce over veal. Top with onion-currant mixture and sprinkle with remaining 1/2 cup cheese.