Tomato pasta sauce

This is an adaptation from various recipes I've used over the years. I'm a big fan of pasta and tomatoes with a sprinkling of Parmesan on top--it's simple, it's easy, and it's satisfying when it's cold and you're feeling hungry and in need of comfort food.

Ingredients:
1 tablespoon olive oil
1 onion, finely diced
1 carrot, peeled and finely diced
1 stalk of celery, finely diced
2 cloves garlic, crushed, peeled, and finely chopped
1 large (28-oz) can crushed tomatoes
1/2 cup chicken broth
sugar
salt and pepper
(optional) dried herbs to taste: I like basil or oregano, though thyme and marjoram would also be good

In a large, heavy pot, heat oil over medium heat and add the onion, carrot, and celery, along with a good pinch of salt and a few grinds of pepper. (Even if you don't care for cooked carrot and celery--I don't, not much--they add flavor to the sauce, so don't skip them. I only recently learned the term mirepoix, and it is a beautiful thing as well as a beautiful word.)  Cook the vegetables for around 5 minutes until somewhat softened, but not browned. Add the garlic and cook for another 2-3 minutes until fragrant.

Add the tomatoes, the chicken broth, and a pinch of sugar, cover, and simmer for 50 minutes over medium-low heat, stirring occasionally. About 5 minutes before the time is up, add your dried herbs. Check seasoning, and serve.

This recipe keeps well in the refrigerator for 4-5 days. It's even better if you let it cool and then warm it up again. I think it would probably freeze well too, though I've not tried this.