Heat oil in a large 3qt. saucepan

Add the onions, (carrots, if desired), (red pepper, if desired), basil, and salt, and simmer on low until the onions are translucent. This is important for sweetness; make sure the onions are translucent.

Add the whole peeled tomatoes, turn up the heat to high, and cook covered for about five minutes. If you cook uncovered, it will burn.

Reduce heat back to low, and mash the tomatoes aggressively with a metal masher (plastic will leech into the sauce).

From here, we have options. If you are looking for a very loose, heterogenous sauce in a hurry, salt to taste and serve now. Otherwise, go to the next step.

If you are serving with a noodle, then you likely want a looser sauce, so keep stirring and mashing for a while, until the sauce is more homogenous. This could be quite a while. Add the water, as needed to thin it out. Salt to taste, and serve.

Alternatively, if you are looking to use the sauce for pizza or macaroni (pasta that is short and not a noodle), then you need to thicken it up. Add the tomato paste, and then stir, and then thin as desired with a little of the water. Salt to taste, and serve.

And if you are just looking to stretch it, add the tomato paste, simmer it all together until you reach the desired consistency, add the water, stir, and reduce to the desired consistency. Salt to taste, and serve.