Toast walnuts in a dry pan over low heat until fragrant. Roughly chop the walnuts, then set aside 1 tablespoon for garnish.
Drain roasted red peppers and add them to a food processor with the toasted walnuts, garlic, breadcrumbs, tomato paste, lime juice, pomegranate syrup, Aleppo pepper, cumin, sumac, salt, crushed red pepper flakes, and 3 tablespoons olive oil.
Pulse ingredients in the food processor until the muhammara dip is mostly smooth with a slightly chunky consistency.
Transfer the dip to a serving plate and smooth the surface with the back of a spoon or spatula, or create decorative swirls. For an extra pop of flavor and color, drizzle with olive oil and pomegranate syrup, then garnish with chopped walnuts, pomegranate seeds, and Italian parsley. Sprinkle the edges with za'atar and serve with Middle Eastern pita bread.
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Notes
For the best muhammara, drain red peppers well before blending so the dip doesn't turn out watery.
Toasting the walnuts brings out their natural flavor and gives the muhammara dip a richer, nuttier taste.
For the best texture, blend until mostly smooth, but leave a little texture from the walnuts rather than turning it completely silky.
Let the dip rest for at least 30 minutes before serving so the flavors have time to meld.
Store leftover Muhammara in an airtight container in the refrigerator for up to 5 days.