Crunchy and warming, sautéed cabbage is a simple dish to serve with pork that doesn’t compete with it. I cook it quickly in butter and olive oil and season it with salt and pepper, plus plenty of lemon juice to keep it bright. Chestnuts are crumbled and fried in butter with a pinch of sugar, then mixed with crunchy panko breadcrumbs as a topping to balance the cabbage with a little holiday richness. Make the breadcrumbs up to three days ahead; warm gently in a skillet just before serving the cabbage.
Heat 2 tablespoons butter and 2 tablespoons olive oil in a large Dutch oven or saucepan over medium-high heat. Crumble the chestnuts into breadcrumb-like pieces, then add to the fat in the pot. Cook, stirring often, until they darken slightly and are crisp, 2 minutes. Sprinkle with the sugar and continue cooking, stirring often, until the sugar lightly caramelizes around the chestnuts, about 30 to 60 seconds. Add the breadcrumbs and continue to cook, stirring often, until they are golden brown and crisp as well, 2 minutes more. Scrape the crumb mixture into a shallow bowl, season with salt and pepper and let cool. Wipe the pot clean with paper towels.
Return the pot to medium-high heat and add the remaining 2 tablespoons of butter and olive oil. Add the cabbage, season with salt and pepper, and cook, stirring every two minutes or so, until wilted and lightly caramelized in spots, but still slightly crunchy, 6 to 8 minutes. Remove the pot from the heat and squeeze the juice from the lemon through a sieve over the cabbage, discarding any seeds.
Transfer the cabbage to a warm serving dish. Stir the parsley into the cooled chestnut breadcrumbs, then sprinkle them over the cabbage. Serve hot.
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