Tuscan Onion Soup with Poached Egg

Heat the olive oil in a large pot or Dutch oven over medium-low. Add the onions, 1 teaspoon salt, black pepper, and bay leaf and cook the onions, stirring frequently. Once they begin to soften, stir in the vinegar.
Partially cover the pot with a lid, and cook the onions until completely soft, about 30 minutes. Stir every few minutes, and ensure the heat isn't too high---you don't want to brown the onions; you only want to sweat them down.
Remove the bay leaf and pour in the beef stock with the remaining ½ teaspoon salt. Bring to a low simmer and heat the stock for 5 minutes. Gently crack the eggs into the soup, spaced apart, and add a pinch of salt and pepper to each. Simmer the eggs gently until they turn white but the yolk is still runny, 4 to 5 minutes.
Ladle the soup into bowls and top each one with an egg. Garnish with grated Pecorino and minced fresh parsley, if desired. You can also drizzle some extra virgin olive oil on top. Serve with crusty or cheesy toasted bread to sop up the egg yolk and stock.