►Arrange a rack in the top third of the oven and heat to 350°F.

►Heat the oil in a 10- to 12-inch cast iron or oven-safe nonstick skillet over medium heat. Add the onions, season with salt and pepper, and cook, stirring occasionally and scraping up any browned bits that accumulate on the bottom of the pan, until the onions are soft and deeply caramelized, about 45 minutes.

►Meanwhile, whisk the eggs, milk, half the Gruyère and half the thyme together in a large bowl. Season with salt and pepper.

►Once the onions are caramelized, stir in the sherry vinegar and scrape up any remaining browned bits from the bottom of the pan. Spread the onions into an even layer and pour the egg mixture over the top. Stir gently once or twice to make sure the onions are evenly distributed among the egg mixture. Sprinkle the remaining Gruyère and thyme evenly over the top. Cook undisturbed until the eggs at the edge of the pan begin to set, about 2 minutes.

►Transfer the skillet to the oven and bake until eggs are just set, about 20 minutes. To check, cut a small slit in the center of the frittata. If raw eggs run into the cut, bake for another minute or two. If not, then the eggs are set. Heat the broiler to HIGH. Broil until the top of the frittata is lightly golden-brown in spots, 2 to 3 minutes. Cool in the pan for 5 minutes, then slice into wedges and serve warm.

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