Halve peppers and scoop out seeds. Place skin-side up on a baking sheet and bake for 20 minutes, until skins are starting to blister. Remove from oven, place in a bowl, and cover with plastic wrap.
While peppers are cooling, toast walnuts in a dry skillet over medium heat until fragrant. Pour walnuts into food processor.
Peel and discard the skins from the peppers, then add peppers to food processor. Add bread crumbs, pomegranate molasses, lemon juice, za'atar, and salt, and process until blended. With the processor running, stream in the olive oil and process until smooth or desired consistency is achieved.
Serve with sliced vegetables, pita, tortilla chips, or whatever you desire.