Heat oven to 350 F. Place garlic, eggplant and peppers on a baking sheet and drizzle with olive oil. Move items around so they are all coated with oil. Roast for about 20 minutes, turn eggplant and pepper over and cook for another 20 minutes or until the skins are charred. Cover and let cool. Cut top and bottom from the eggplant and peppers and remove peel. Pop the garlic cloves out of the peels.
Put eggplant, pepper and garlic in a food processor (you can also use a bowl with an immersion blender). Slowly add ¼ cup olive oil while blending. When mixed well, add vinegar and paprika. Blend well again.
Transfer ajvar to a medium sauce pan and let simmer for about 20 minutes. Add salt and pepper to taste. Serve at room temperature and store in an air tight container in the refrigerator.
Serve with grilled lamb or sausages.