Put the eggplant in a strainer and sprinkle the cubes with salt. To get all of the bitter liquid out: add a plate on top of the cubed eggplant and some kind of weight on top of that to pushit down (I use my full tea kettle) and leave them to rest for about half an hour.
In the meantime, wash and slice the other vegetables as indicated.
In the pre-heated pressure cooker, on high heat without the lid, add the olive oil and brown the vegetables, adding them in the following order, stirring them constantly with a wooden spoon.
First, add the eggplant and potatoes (wait 3 Minutes but keep stirring), peppers and onions (wait another 3 Minutes and keep stirring), Zucchini (stir for another 3). Your cooker will begin to get quite full, so stir carefully!
Finally, add half the chopped basil, pine nuts, raisins, olives, capers, salt and pepper to taste.
If you're using an electric pressure cooker, that requires more than ½ cup of water to reach pressure, add one cup of water. Close the lid and set the valve to pressure cooking position. Electric pressure cookers and stove top pressure cookers: Cook for 4 Minutes at High Pressure.
When time is up, open the pressure cooker with the Normal release - release pressure through the valve.
Transfer the contents of the pressure cooker to a serving dish immediately (so the vegetables can cool) and the caponatina come to room temperature before mixing in the cherry tomatoes and dressing with a little fresh olive oil, balsamic vinegar (if needed - check to taste the acidity first - the tomatoes if not fully ripe may have contributed enough acid).