If using fresh peppers, turn 2 gas burners to the highest setting and set 1 medium red bell pepper directly on each flame. Use a pair of tongs to turn the pepper occasionally until the skin is completely blackened, about 8 minutes. (If you don’t have a gas stove, roast them in the broiler or on the grill). Transfer to a heatproof bowl and cover with plastic wrap, aluminum foil, or a pot lid. Let the peppers steam and cool while you toast the walnuts.
Arrange a rack in the middle of the oven and heat the oven to 350°F.
Spread 1/2 cup walnuts out in a single layer on a rimmed baking sheet. Bake, tossing halfway through, until toasted and fragrant, 8 to 10 minutes total. Transfer to the bowl of a food processor fitted with the blade attachment. Pulse until coarsely chopped, about 10 (1-second) pulses. Transfer 2 teaspoons chopped walnuts to a small bowl and reserve for garnish.
Prepare the following, adding each to the food processor as you complete it: Remove and discard the skin of the peppers with your fingers (it’s okay if a few blackened bits of the skin remain). Remove and discard the stem and seeds, then tear the peppers into large strips (1 1/2 cups). (If using jarred peppers, tear 1 1/2 cups into large strips.) Smash and peel 1 garlic clove. Squeeze the juice of 1/2 small lemon until you have 1 teaspoon juice.
Add 1/2 cup fresh bread crumbs, 2 tablespoons olive oil, 2 tablespoons pomegranate molasses, 1 teaspoon Aleppo pepper flakes, 1/2 teaspoon kosher salt, 1/4 teaspoon ground cumin, and 1/4 teaspoon granulated sugar. Pulse, scraping down the sides of the bowls as needed, until the muhammara is uniform and mostly smooth but still a bit rustic and chunky, about 25 (1-second) pulses. Transfer to a serving bowl and garnish with a drizzle of pomegranate molasses and the reserved walnuts.