Make sauce. Combine all ingredients in small bowl. Refrigerate until ready to use.
For sandwiches: Heat butter in heavy medium skillet. Add onions, tossing to coat with butter. Cook over low heat, stirring occasionally, for about 20 minutes or until onions are soft and caramelized. Salt and pepper to taste. Keep warm.
Brush griddle or heavy skillet with cooking spray or unflavored oil. Heat until almost smoking. Split sausages lengthwise and place cutside-down on griddle. Turn when browned, and brown skinned-side, cooking until heated through.
Split rolls or baguette slices lengthwise. Spread the cut sides (tops and bottoms) generously with prepared sauce. Spread about 1/4 cup of shredded lettuce on each roll bottom. Top each with 1/4 of onions. Sprinkle Provolone shreds over, dividing equally over the 4 bottoms. Place sausage halves on top of cheese and place roll tops over. Serve hot pepper sauce on the side, if you desire.