- Heat the broiler (top element) of your oven. Core both cabbage halves. Roughly shred the cabbage, using a sharp knife, a mandoline, or the shredding blade of a food processor.
- Place in a large bowl and toss, lightly, with olive oil and spread in one thick layer on a big baking sheet.
- Broil for 5 to 7 minutes, or until the tips of the cabbage shreds begin to char. Stir thoroughly to turn the cabbage, then broil for an additional 5 minutes. You are not cooking the cabbage completely through you are trying to add as much color and crispiness to the edges as possible.
- Remove the cabbage from the oven and set aside to cool for a few minutes. Turn the oven to bake and down to 350°F.
- Roughly chop the hazelnuts and spread in a baking dish. Bake for 5 to 10 minutes or until lightly toasted (watch closely — the size of the hazelnuts, the baking dish, and your oven will all determine the actual roasting time).
- Whisk together 1 tablespoon olive oil, the juice of 1 lemon, and the honey.
- Toss the semi-cooled and wilted cabbage with the dressing and salt and pepper to taste.
- Toss with 1 cup of the toasted hazelnuts.
- Spread on a large platter and garnish with the remaining 1/4 cup of hazelnuts. If desired, also garnish generously with shaved Gruyere cheese.
- Serve warm or at room temperature.
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