De-stem the red bell peppers, then cut them in half lengthwise. Remove the seeds and membrane from each half. Cut the eggplant in half lengthwise.

Place the vegetables, skin-side up, on a foil-lined baking sheet. Then place the baking sheet in the oven. Broil the vegetables until the bell peppers blister (they should blacken slightly, which gives the sauce an earthier flavor) and the eggplant has softened.

Remove the baking sheet from the oven. While hot, place the peppers in a glass mixing bowl and cover the bowl with plastic wrap to steam the peppers. Steam them until the peppers cool. This will help the peeling process later.

Spoon out the flesh of the eggplant (remove large seeds along the way) and place the flesh in a food processor. Add the Kalamata olives and garlic to the food processor as well. Process the vegetables until smooth.

Uncover the bell peppers, then peel off the skin (as much as possible). Place the bell peppers in the processor with the sauce. Pulse chop the peppers to form a chunky sauce.

Pour the sauce into a bowl, then add the white wine vinegar, smoked paprika, and cayenne pepper. Stir to combine. Then add salt to taste.

Serve immediately, or for best flavor allow the ajvar sauce to chill covered in the refrigerator for 2 to 3 hours to allow the flavors to meld.