Puree onion and garlic in a food processor, or finely chop with knife.
Cover bottom of large pot (I use an 8 quart but my sister uses a 10 quart; then again, she always makes more sauce than I do) with olive oil and saute the pureed onions and garlic until they’ve caramelized, about 5 – 10 minutes. One thing I've noticed about sauteing pureed onions and garlic is that they tend get a little bluish. I threw mine out the first time it happened. They're fine, though, so use 'em.
Puree the carrots and celery in a food processor or finely chop with a knife.
Add the carrots and celery to the pot with the onions and garlic, plus a little more olive oil if the vegetables look dry, and saute for another 5 – 10 minutes.
Add tomato paste and cook for approx. 5 minutes, stirring frequently.
Add red wine and cook approximately 10 minutes to evaporate the alcohol.
Optional: if you prefer a smooth sauce and weren’t able to find pureed tomatoes, puree the tomatoes in a food processor.
Add the tomatoes, herbs, and chicken bullion to the pot. Also add salt and pepper to taste.
Cook sauce until it reduces to about 3/4 of original (2-3 hours on stove on low heat). Stir occasionally and check seasonings about midway through. If the sauce tastes too bitter or acidic, add more chicken bullion or some chicken stock and then adjust the seasonings to taste. Also, if it gets too thick, add chicken stock and then adjust seasonings to taste.