Preheat the oven to 325 degrees. Toast the walnut pieces for 14 minutes. Remove the walnuts and raise the temperature to 425 degrees. Place the peppers in a large saute pan or baking sheet. Roast for 25 minutes until most of the skin is blackened; turning about halfway through the roasting process.
Remove the peppers from the oven and cool them. Peel the blackened skin off and carefully discard any seeds; reserving the juices if you are able to do so.
Process the walnuts in a food processor until coarsely chopped. Add the remaining ingredients and process until chunky or smooth (your preference). Thin with the reserved pepper juice, water, or lemon juice if necessary.