How to Make It
Preheat the oven to 400°. Put the walnuts on a rimmed baking sheet and toast in the oven for about 4 minutes, or until lightly browned. Transfer the nuts to a plate to cool completely. In a small food processor or mini-chopper, combine the nuts with 1/2 cup each of the parsley and cilantro, the garlic and a large pinch each of salt and pepper. Process to a paste. Add 3 tablespoons of the olive oil and process briefly to blend. Scrape the mixture into a small bowl and cover with plastic wrap.
In a large skillet, warm 1 1/2 tablespoons of the olive oil over high heat. Add half of the mushrooms, season with salt and pepper and cook, stirring, until browned, about 3 minutes. Reduce the heat to low and cook the mushrooms until the liquid evaporates and they brown again, about 8 minutes. Transfer the mushrooms to a large plate and repeat with the remaining 1 1/2 tablespoons of olive oil and mushrooms. Season with salt and pepper.
Return all of the mushrooms to the skillet and add 1/2 cup of the nut paste. Stir in the chicken stock, 1 tablespoon at a time, to make a sauce. Season with salt and pepper and transfer the mushrooms to a large shallow dish. Serve warm or at room temperature, sprinkled with the remaining 1 tablespoon each of parsley and cilantro.