Prepare the water bath canner, jars, and lids. Fill the canner and set it over heat before you start prepping, since it takes a long time to reach a boil.
Heat the oven to 400 degrees F and line three rimmed baking sheets with foil. Leave the tomato sheet ungreased.
Wash and core the tomatoes, cut them in half, and arrange them on the first sheet. Roast about 45 minutes, until the skins just begin to char.
Halve and seed the bell peppers and set them skin side up on the second sheet. Quarter the onions with the skins on and add them skin side up and add them to the second sheet.
Cut the eggplant into 1 inch cubes and scatter them around. Spray the sheet lightly with oil. Add them to the third baking sheet.
Roast the second and third sheet about 30 minutes, until the eggplant is golden and the peppers are tender.
Let everything cool on the pans until you can handle it, then slip the skins off the tomatoes, peppers, and onions and discard them.
Chop the tomatoes coarsely, keeping the seeds and juice, and put them in a stock pot that holds at least 6 quarts.
Coarsely chop the roasted onions and peppers and add them to the pot along with the roasted eggplant.
Add the wine, balsamic vinegar, olives, capers, garlic, anchovy paste, salt, oregano, and black pepper. Stir well.
Bring the pot to a boil, then reduce the heat and simmer uncovered for 15 minutes.
Taste and adjust the dried seasonings if you want to. Leave the wine, vinegar, and vegetables as written.
Ladle the hot sauce into hot jars, leaving 1/2 inch headspace.
Release trapped air bubbles, check the headspace again, and wipe the rims and threads clean.
Set the lids on and apply the bands fingertip tight.
Process pints for 45 minutes in a boiling water bath canner, adjusting for altitude (see notes).
Turn off the heat and let the jars rest in the canner for 5 minutes before lifting them out.
Cool the jars undisturbed on a towel for 12 to 24 hours, then check the seals, remove the rings, label the jars, and store them in a cool, dark place.