Place an oven rack on the top third of the oven and set the broiler to high.
Place the Ajvarski/bell peppers and red chili pepper on a baking sheet.
Cut the stem off the eggplant and discard. Slice the eggplant in half lengthwise, then crosswise to make four pieces. Place the eggplant pieces on the baking sheet with the peppers skin-side up.
Place the baking sheet on the oven rack under the broiler and cook, turning the peppers occasionally, until the skin on all sides starts to char and wrinkle.
Transfer the peppers and eggplant to a large bowl and cover the top with plastic wrap or place in a heat-safe large plastic bag and seal shut.
Allow the vegetables to rest for 15 minutes.
Peel the skin off the peppers and eggplant and discard. Remove the stems and seeds.
Place the peppers and eggplant in a large food processor. Add the garlic, salt, and pepper.
Pulse the mixture until smooth.
Add the olive oil and vinegar. Continue to pulse until well incorporated. Adjust seasonings to taste.
Transfer the mixture to a medium saucepan and place over medium low heat.
Simmer the sauce, stirring often, until it starts to thicken, about 20 minutes. Adjust seasonings.
Allow to cool, then transfer to an airtight container and refrigerate for up to 4 days.