Peel the onions and trim the root and stem ends. Slice each onion in half from pole to pole, lay the flat side down and slice across into 1/8–1/4-inch (3–6 mm) thin, even slices. Aim for uniform thickness so they cook evenly.

Heat the pan

Place a wide heavy-bottomed skillet (preferably stainless steel or cast-iron) over medium heat. Add the oil and butter. Heat until the butter melts and begins to foam but does not brown (about 1–2 minutes).

Add onions and begin cooking

Add all sliced onions to the pan and stir to coat them with the fat. Spread them into an even layer and let them cook, stirring every 2–3 minutes for the first 10 minutes so they soften and begin to sweat without browning. Sprinkle 1 teaspoon kosher salt and 1 teaspoon granulated sugar over the onions and stir to combine (the sugar helps with color and caramelization).

Caramelize slowly

Reduce heat to medium-low. Continue cooking, stirring every 3–5 minutes and scraping up any brown bits from the pan. After about 25–35 minutes the onions will be soft, deep golden and starting to stick in places. If they brown too quickly or begin to catch, add 1–2 tablespoons water (or broth) and lower the heat further to prevent burning. Continue this low-and-slow process for a total of 35–45 minutes, depending on desired color and depth of flavor.

Deglaze and finish

When the onions reach a rich amber-brown color and have a jammy texture, pour in 60 ml (about 1/4 cup) water or low-sodium broth and scrape the browned fond from the pan with a wooden spoon. Stir in 1 tablespoon sherry vinegar (if using) to brighten the flavor. Taste and adjust seasoning with freshly ground black pepper and additional salt if needed.

Cool and store

Transfer the caramelized onions to a bowl and cool slightly before using. They can be used immediately, refrigerated in an airtight container for up to 5 days, or frozen in portions for up to 3 months.

Optional finishing & uses

Herb finish: Stir in 1 tablespoon fresh thyme leaves in the last minute of cooking for an herbal note.

Balsamic finish: Drizzle 1 tablespoon balsamic reduction or glaze over the finished onions and toss to coat for a sweeter, tangy finish.

Serving suggestions: Use these caramelized onions on burgers, pizzas, grilled cheese, stirred into mashed potatoes or pasta, folded into quiches and tarts, or served alongside roasted meats. Reheat gently in a skillet or microwave before using.