Place 2 ½ lb red bell peppers and ¾ lb eggplant on a parchment paper lined baking sheet. Place this sheet in the oven and broil the vegetables until the outside is charred and the vegetables are soft.
Place the vegetables in a large bowl and cover the bowl with plastic wrap to give the skin time to sweat. Allow the vegetables to rest for at least 30 minutes to make it as easy as possible to remove the skin.
When ready, peel the peppers and eggplants and remove the seeds. This will keep the color of the ajvar that bright red color.
Place the peeled vegetables in a colander and allow them to drain for at least two hours, but preferably overnight. Stir occasionally to allow the liquid to drain.
Run the peppers, eggplant and 3 garlic cloves through a food processor and blend until the blend is mostly smooth with some chunks.
Add ¼ cup sunflower oil into a pot or pan and allow it to warm. Then add the pepper and eggplant puree and cook it until the mixture thickens. You will know it is ready when you can drag a spoon through it and it leaves a mark behind. This took about 10 minutes for me, but can take up to 45 minutes.
Add 1 Tbsp white vinegar, 1 tsp salt, and ½ tsp granulated sugar, and mix until combined. Cook for another 3-4 minutes.
Allow the ajvar to cool to room temperature, then serve and enjoy!