Quick-n-Dirty Vegetable Sauce

For a couple of zucchini and 12 oz of mushrooms, one standard can (16 oz?) of sauce is enough. Good veggies for this: mushroom, zucchini, broccoli, spinach, artichoke heart, green bean, acorn squash. Peppers and onions added to the sauté overwhelm the whole dish for me, making it taste like a big pepper (rather than a big tomato which is what I want it to taste like).

The Saturday afternoon way to get good veggies in sauce (a sauté pan, a pot,