Place tomatoes in large saucepan and boil for 25 minutes uncovered. Allow cooling slightly then process through a food mill or sieve to remove skins and seeds.
In a large skillet, heat olive oil and sauté onions, garlic, and mushrooms until tender.
Place the sautéed vegetables in a stockpot, add tomatoes and remainder of ingredients and bring to a boil. Lower heat and simmer, uncovered for approximately 25 minutes or until desired thickness, stirring frequently to avoid burning.
Skim any foam from the top of the sauce as you stir. Taste and add more brown sugar if desired as tomatoes vary in tartness.
If more sugar is added bring to a simmer for 5 more minutes. Remove bay leaves. Ladle into jars leaving 1 inch of headspace.
Cap and seal. Place in the canner with 2 to 3 inches of hot water.
Pressure cook for 25 minutes on High pressure. Once done, allow pressure to come down naturally before opening the cooker.