How to Make It
Preheat the oven to 350°. Spread the walnuts in a pie plate and bake for 8 minutes, until golden and fragrant. Let cool, then coarsely chop.
Meanwhile, in a food processor, process the bread to form coarse crumbs. In a medium skillet, heat 3 tablespoons of the olive oil. Add the garlic clove and cook over moderately low heat until golden, about 5 minutes. Discard the garlic clove. Stir in the anchovies and capers and cook, breaking up the anchovies, until the capers are crisp, about 1 minute. Add the red pepper and cook for 30 seconds. Stir in the bread crumbs and cook, stirring a few times, until golden and crisp, about 4 minutes. Transfer the bread crumbs to a plate and let cool. Stir in the walnuts.
In a food processor fitted with a slicing blade, coarsely shred the brussels sprouts. In a large skillet, melt the butter in the remaining 1 tablespoon of olive oil. Add the onion and cook over moderately high heat until softened, about 4 minutes. Add the brussels sprouts and cook, stirring a few times, until browned in spots, about 6 minutes.
Add the chicken stock to the skillet and cook over moderate heat, scraping any browned bits from the bottom, until the skillet is dry and the brussels sprouts are tender, about 4 minutes. Season the brussels sprouts with salt and pepper. Transfer them to a bowl, sprinkle with the bread-crumb mixture and serve.