Combine the peppers, walnuts, and garlic in a food processor and blend until smooth, about 3 minutes.
Add all of the remaining ingredients except the olive oil and pulse until smooth, about 2 minutes. Turn off the processor and scrape down the sides of the bowl as you go.
With the processor running, add the olive oil slowly and blend until the oil is completely incorporated. Taste for seasoning.
Transfer the muhammara to a bowl and serve chilled or at room temperature with your favorite bread. It will keep, refrigerated, for several days.