Preheat the oven to 325°F.
Place hazelnuts on a baking sheet and put them in the oven to toast them up, about 10-12 minutes -- your nose will know when they are done. Remove them from the oven and cool. Run your knife through them once, chopping them coarsely.
While the nuts are toasting up, place a large skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the onions, season with a little salt and pepper, and cook, stirring frequently for 10 minutes. Add 1 tablespoon of the balsamic vinegar and a big splash of water. Use a wooden spoon to scrape up any bits on the bottom of the pan and cook for about 1 minute.