Roast the eggplants and red peppers until the skin is charred and the flesh is fully cooked. This can be done on a wood burning grill, in an oven, or over a fire in a cast iron pot.
Once roasted, place the eggplants and peppers in a pot with a lid and let them sit for 30 minutes to steam.
While the vegetables are steaming, peel, wash, and finely chop the onions.
Peel, wash, and grate the carrots and parsnips.
Peel and chop the garlic.
After steaming, peel the charred skin off the eggplants and peppers. Collect any juices that drip from them.
Chop the peppers into small pieces, but do not make them into a paste.
Chop the eggplants by hand into small pieces. Do not use a food processor or blender for the eggplants.
In a large pot, heat the oil over medium heat.
Add the onions, peppercorns, laurel leaves, herbs, tomato sauce, and tomato paste. Mix well and cook for 15 minutes until the onions are soft.
Add the grated carrots and parsnips to the pot. Cover and cook for 15 minutes.
Add the chopped eggplants and red peppers (and any collected juices) to the pot. Mix well.
Cook on low heat for 40 minutes, stirring every 5 minutes to prevent sticking.
In the last 5 minutes of cooking, add the garlic, salt, brown sugar, and ground pepper. Mix well and simmer.
Remove the pots from the heat and let the mixture cool for 15 minutes.
Fill sterilized jars, leaving about 4 cm (almost 2 inches) of headspace.
Can the jars using a method that ensures a long shelf life (details not provided in text).
After canning, allow the jars to cool slowly, ideally for at least 24 hours, by wrapping them in blankets.
