Preheat 2 tablespoons of oil in a large skillet over medium heat. Add the onions, and sweat slowly for about 5-7 minutes until translucent. Add the mushrooms and continue to sauté until the mushrooms have cooked down, and the mixture is golden brown and fragrant. The volume of vegetables in the pan should be considerably reduced from when you started. Let cool at least 10 minutes. 

 Add the mushroom and onion mixture to a food processor. Drain the nuts, and add them as well. Begin to chop the mixture in the processor, and stream in the oil and vinegar while the machine is running. Add the salt and pepper, and pulse again to combine. Taste for seasoning. The mixture should chopped very, very finely, and should be fairly smooth (but not entirely pureed). Refrigerate until ready to serve.