I love Chef Mamoru Kataoka's recipe and read that he sweats onions slowly for 1 hour. Up until then I made tomato sauce without cooking the onion for that long, but I tried it and I was struck by the difference in the depth of flavor of the sauce.

If you sauté the onion slowly until a lot of flavor seeps out, you can make a delicious sauce without having to add a soup stock cube.
Stirring the pot slowly while you're surrounded by the fragrance of the onion is a nice experience. Recipe by Yukijirushi