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Heat 2 tablespoons butter in a large, deep-sided pot over medium heat. Add 1 clove garlic and the panko, and sprinkle with sea salt and pepper. Toast, stirring often, until panko is a light golden hue. Scrape out of pot and set aside.
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To the same pot, add the remaining 4 tablespoons butter; when melted, stir in the onion, 1/4 teaspoon sea salt and several twists of pepper. Cook onion until tender, about 5 minutes. Fold in garlic, chili, and anchovies, and cook 1 minute more. Add the cabbage and Brussels sprouts in batches, sprinkling with sea salt as you go. Once vegetables have wilted, cook, stirring often, until they're a deep golden hue, 20 - 25 minutes.
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Meanwhile, bring a large pot of water to a boil. Add several tablespoons sea salt and cook pasta to al dente. Reserve about 2 cups pasta water, and drain.
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Toss cooked pasta with the vegetables. Add cheese and all but 2 tablespoons parsley. Taste and add sea salt or pepper as needed. Drizzle in about a cup pasta water so that things are creamy and a little saucy. Spoon onto a large platter and top with toasted panko, parsley, and a pinch of red peppers flakes. Serve right away.