If possible, cook the eggplant and red peppers on a grill/barbecue, turning now and then until the skin on all the vegetables has blackened on all sides and the vegetables are tender. If you can't grill them, you can get a similar effect by cooking over a gas flame on the stove, carefully turning regularly. Alternatively, place on a baking sheet and bake around 15 minutes at 425F/220C, finishing under the broiler/overhead grill as needed. If cooking in oven, and if risk of sticking to grill, lightly brush with olive oil before cooking.
Allow the cooked eggplant and peppers to cool a minute then place in a freezer bag and close/fold over and allow to stem as they cool. Leave them around 10 minutes. Then, peel off and discard the skin on all the vegetables and remove the stem from the eggplant and core along with all the seeds from the peppers. You may find liquid has collected in the peppers - just pour this off as you go.
Place the eggplant and pepper flesh in a food processor/blender and add the rest of the ingredients - peeled garlic, olive oil, vinegar, salt and pepper). Pulse a few times until fairly smooth. Try it and adjust seasoning to taste.
Transfer the mixture to a small pot/pan and warm to a simmer. Continue to cook on a low heat for around 20 minutes to allow the mixture to dry slightly so there's no obvious liquidy texture. Allow the mixture to cool then transfer to a jar and store in the fridge until needed (can be stored around 3 - 5 days).
Video
Notes
Use sweet red bell peppers for this - traditionally the local pepper is often called Ajvarski or red bull horn pepper (due to their shape) but other mild, sweeter red peppers also work.