I actually make mine using pretty much the same ingredients, but halve and roast the tomatoes in a low oven, then add the sweated down garlic and onion, blend smooth with a stick blender then add fried diced courgette and chopped herbs (usually parsley but that's mainly because I've usually got more of that than basil.)
Don't know whether part roasting the tomatoes actually improves the flavour, but it does take away the long wait for it to reduce down and wondering whether it's going to start sticking to the pan.