Preheat your oven to 400°F (200°C).
Place the eggplants on a baking sheet and roast in the preheated oven for about 30-40 minutes, turning occasionally, until the skin is charred and the flesh is soft.
While the eggplants are roasting, place the red bell peppers on another baking sheet and roast them for about 20-25 minutes, or until the skins are blistered and blackened.
Once roasted, remove the eggplants and peppers from the oven and let them cool. Peel the skins off both vegetables and discard the seeds and stems. Dice the flesh of the eggplants and peppers into small pieces.
In a large pot or Dutch oven, heat the vegetable oil over medium heat. Add the chopped onion and cook until it becomes translucent, about 5-7 minutes.
Add the minced garlic and cook for another minute until fragrant.
Stir in the diced tomatoes, tomato paste, and sugar. Cook for about 10 minutes, stirring occasionally, until the mixture thickens slightly.
Add the diced eggplants and red bell peppers to the pot. Stir well to combine.
Add the white vinegar, dried thyme, bay leaf, salt, and black pepper. Mix thoroughly.
Reduce the heat to low and let the mixture simmer for about 30-40 minutes, stirring occasionally, until it thickens to a spreadable consistency.
Remove the bay leaf from the Zacuscă.
Allow the Zacuscă to cool before transferring it to sterilized jars for storage.
Enjoy your meal!