Preheat oven to 350°. Toast walnuts on a rimmed baking sheet, tossing halfway through, until golden brown and fragrant, 8–10 minutes. Let cool. Pick out a few walnuts for serving and coarsely chop; set aside.

Meanwhile, place a rack in upper third of oven and heat broiler. Broil bell peppers on a rimmed baking sheet, turning occasionally, until skins are charred and flesh is softened, 12–15 minutes. (Alternatively, you can char over a gas burner on medium-high, turning occasionally with tongs, 12–15 minutes.)

Transfer bell peppers to a medium bowl and cover tightly with plastic wrap so that they steam, 10 minutes (this extends the cooking and also makes it easier to remove the skins).

Remove skins from bell peppers (it’s okay if some bits don’t come off); remove and discard ribs and seeds. Pulse bell peppers, breadcrumbs, oil, Aleppo-style pepper, tahini, lemon juice, paprika, toasted walnuts, and 2 Tbsp. pomegranate molasses in a food processor until mostly smooth; season muhammara with salt.

Transfer muhammara to a small bowl; drizzle with more pomegranate molasses and top with reserved chopped walnuts.