Heat 2 tablespoons olive oil in a heavy-duty pot over medium-high heat. Add onions and reduce the heat to medium. Cook, sitrring occasionally until the onions begin to brown, about 5 to 7 minutes.
Sprinkle with 1/2 teaspoons salt and continue to cook, scraping the bottom of the pot frequently until the onions are well browned, 20 to 30 minutes. Add the ale and bring to a boil over high heat. Reduce the heat slightly and simmer until most of the ale has evaporated; about 2 minutes. Add the vegetable broth and simmer for 10 minutes to allows the flavors to blend.
Preheat the oven to 425 degrees. On a rimmed baking sheet, toss the bread cubes with the remaining 2 tablespoons olive oil. Spread in a single layer until golden. Bake for 7 to 10 minutes.
Remove from the oven, push the bread cubes closely together and sprinkle with the cheese. Bake until the cheese is melted and bubbly, about 3 minutes.
Sprinkle with parsley or chives.