brussels sprouts, quartered
extra virgin olive oil
salt and freshly ground black pepper
fresh lemon juice
pure chile powder, such as ancho
red cabbage, very thinly sliced on a mandoline
garlic cloves, thinly sliced
Parmigiano-Reggiano cheese, thinly shaved
Preheat the oven to 450°. Spread the pine nuts in a pie plate and toast for about 3 minutes, until golden brown. On a large rimmed baking sheet, toss the brussels sprouts with 1 tablespoon of the olive oil and season with salt and black pepper. Roast for about 15 minutes, until the brussels sprouts are lightly caramelized and tender.
Meanwhile, in a small bowl, whisk the lemon juice with the honey, mustard, cayenne and chile powder. Slowly whisk in 1/4 cup of the olive oil and season with salt and pepper.
In a large bowl, toss the cabbage with the toasted pine nuts and cranberries. In a small skillet, heat the remaining olive oil. Add the garlic and cook over moderate heat until golden, about 1 minute. Scrape the garlic and hot oil over the cabbage. Add the brussels sprouts and toss, then add the dressing and toss again. Scatter the cheese shavings over the top and serve right away.