Heat 2 tablespoons oil in heavy large skillet over medium-high heat. Add onions and saute until slightly softened, about 5 minutes. Stir in vinegar, sugar and caraway seeds. Reduce heat to medium-low and saute until onions are deep brown and very tender, about 20 minutes longer. Season to taste with salt and pepper. (Can be prepared 2 hours ahead. Let stand at room temperature. Rewarm over low heat before using.)
Preheat broiler. Brush 11x7-inch metal baking pan with oil. Place sausages in pan. Broil until sausages are brown and crisp, about 6 minutes per side. Transfer sausages to work surface and cut lengthwise in half.
Arrange 3 sausage halves on each of 2 bread slices. Spread 2 teaspoons mustard over sausages on each. Top sausages with caramelized onions, dividing equally. Top with Gruyère or Emmenthal cheese slices, dividing equally. Cover with remaining 2 bread slices. Spread half of butter over upper bread slices.
Heat large nonstick skillet over medium-low heat. Carefully invert sandwiches, buttered side down, into skillet. Cover and cook until bottoms are brown, about 5 minutes. Spread remaining butter over upper bread slices. Turn sandwiches, cover and cook until bottoms are brown, about 4 minutes longer.