Preheat the oven to 425°F.
Lightly brush the bell peppers with 1 tablespoon of olive oil and place them in a greased oven-safe pan or cast-iron skillet. Roast in the preheated oven for about 30 minutes, turning them occasionally to ensure even charring. The skins should blister and darken, imparting a deep, smoky flavor.
Once roasted, transfer the peppers to a bowl and cover tightly with plastic wrap. Let them sit for a few minutes to allow the steam to loosen the skins. When cool enough to handle, peel off the skins, discard the seeds, and slice the peppers into thin strips.
In a large food processor, combine the roasted red pepper strips with the remaining 3 tablespoons of extra virgin olive oil, walnuts, tomato paste, bread crumbs, pomegranate molasses, garlic, Aleppo pepper, sugar, sumac, salt, and cayenne (if using). Blend until the mixture forms a smooth, creamy paste with a slightly textured consistency.
Transfer the muhammara to a serving bowl. If making in advance, cover and refrigerate, but allow it to come to room temperature before serving for the best flavor.
Just before serving, drizzle with extra virgin olive oil and garnish with additional walnuts and fresh parsley if desired. Pair with warm pita bread or crunchy pita chips for a deliciously rich and tangy dip.