Cut each pepper into quarters and remove and discard the core and seeds. Place skin-side up under a preheated high grill and cook until the skin is blackened. Transfer to a food bag and leave until cool enough to handle.
Remove and discard the blackened skins from the peppers and place the pepper flesh on kitchen paper to remove the excess moisture.
Place the walnuts in a food processor and process until finely ground. Add all the remaining ingredients, then process until smooth.
Scrape the mixture into a bowl and season to taste with salt and pepper.
Serve garnished with pomegranate seeds and mint leaves, with warmed flatbreads, if liked.