In a medium skillet over medium heat, melt the butter. Add onion slices and stir to coat with butter. Sprinkle the onions with salt. Stir until onions until they cook down and begin to turn golden, about 5 minutes. Add sugar and continue to stir until onions darken to a medium golden color and turn translucent, about 5 more minutes. Add balsamic vinegar, scrape up the bits from the bottom of the pan and turn heat to low. Heat until most of the liquid absorbs, about 5-7 more minutes. Taste and season with more salt if needed, then serve. For richer flavor, the onions can be cooked for up to an additional 45 minutes if desired. Serve in soups or casseroles or on salads, burgers, sandwiches, steaks and eggs. Store in refrigerator for up to three days or freeze.