Blacken the peppers and eggplants: If you have a gas range you can turn the burner on and blacken the pepper and eggplant skins directly on the flame, using tongs. Otherwise, turn your oven to broil and on a metal baking sheet, place the peppers and eggplants and let them turn black. Check the peppers every 8 – 10 minutes or so, turning them as needed to be sure all the skin gets charred. The same for the eggplants but they will take longer. My oven is a bit weak so they took about 40+ minutes to fully char.
When you remove the pepper and eventually eggplants, put each in a bowl and cover with aluminum foil for at least 5 – 10 minutes to steam and cool. When they are cool enough to handle peel the skin off the peppers, discarding the skin and seeds, reserving the roasted pulp. Depending on how your eggplants char (i.e. soft charred skin or hard charred shell), in either case you want to remove the smoked pulp of the eggplant and reserve, and discard the skin.
In a blender or food processor, add the pepper and eggplant pulps, crushed garlic, olive oil, vinegar, and a dash of salt and pepper. Blend until smooth.