2 large yellow onions, thinly sliced

1 1/2 teaspoons kosher salt, divided

1 tablespoon balsamic vinegar

8 large eggs

1/4 cup whole or 2% milk

1 tablespoon Dijon mustard

1/4 teaspoon freshly ground black pepper

1/2 cup diced Gruyere cheese (2 ounces)

1 tablespoon finely chopped fresh chives

Arrange a rack in the middle of the oven and heat to 400 F.

Heat 1 tablespoon of the butter in a 10-inch cast iron skillet over medium heat until bubbling. Add the bread cubes to the pan, toss to coat with the butter, and arrange in a single layer. Toast the bread, tossing every minute or so, until the bread cubes are golden-brown on all sides, about 5 minutes total. Transfer the croutons to a bowl; set aside.

Reduce the heat to low. Add the oil, onions, and 1/2 teaspoon of the salt to the same skillet. Cook, stirring every 5 to 10 minutes and scraping any browned build-up from the bottom of the pan, until the onions are soft and deeply browned, about 40 minutes total. Add the vinegar and scrape up the browned bits at the bottom of the pan.

Whisk together the eggs, milk, mustard, remaining 1 teaspoon salt, and pepper in a large bowl. Stir the remaining butter and croutons into the skillet, then spread in an even layer. Pour the egg mixture over the top. Tilt the pan to make sure the eggs settle evenly. Top with the cheese. Cook until the eggs at the edges of the skillet begin to set, 2 to 4 minutes.

Bake until the eggs are set, 8 to 10 minutes. To check, cut a small slit in the center of the frittata. If raw eggs run into the cut, bake for another few minutes; if the eggs are set, pull the frittata from the oven.

Cool in the pan for 5 minutes, top with chives, then slice into wedges and serve warm.

Recipe notes: The croutons can be made up to one week in advance and stored in an airtight container at room temperature. The caramelized onions can be made up to three days in advance and stored in an airtight container in the refrigerator, or up to three months in advance and stored in the freezer. Leftovers can be stored in a covered container in the refrigerator for up to five days.

(Kelli Foster is assistant food editor for TheKitchn.com, a nationally known blog for people who love food and home cooking. Submit any comments or questions to editorial@thekitchn.com.)