Place a large pot on the stove over medium-high heat. Add the olive oil and let it heat just until it begins to shimmer
Add the onions and cook for 2-3 minutes, until they start to develop some color.
Add the eggplant and stir to incorporate. Finally, add the zucchini and garlic and stir to combine.
Cook for 3-4 minutes, until the vegetables start to color. Add the tomato sauce, water (the best way to do this is to pour the water into the sauce jar and give it a swirl, so that you don't lose any flavor), salt and pepper and stir to combine.
Reduce the heat to medium-low, cover, and cook for 45 minutes to an hour, until the vegetables have softened, but haven't lost all identity.
Remove the lid, increase the heat a little, and simmer more actively to cook off any watery liquid that might have accumulated on the surface of the braise.
Taste and adjust the salt and pepper levels, as needed.
Serve over cooked polenta or pasta and top with grated Parmesan cheese.
If you can, make this braise the day before you want to serve it, as it improves overnight in the fridge.