Add 1 tablespoon olive oil to a large skillet. Lower to medium low. Add onions and cook for 15 minutes, stirring occasionally, until softened and golden. Add splash of water if onions begin to burn or stick. Remove onions.
In the same skillet or sauté pan, heat 2 tablespoon olive oil over medium-high heat. Add mushrooms and ¼ teaspoon salt. Let them cook undisturbed for about 5 minutes, then stir occasionally for another 5. Increase temperature to high and cook until they've released most of their liquid and start to brown.
Lower heat to medium. Add the onions. Stir in garlic, thyme, oregano and black pepper. And salt to taste. Cook 1 minute until fragrant.
Stir in tomato paste and cook for 2 - 3 minutes, stirring constantly. Add crushed tomatoes, mushroom broth, balsamic vinegar, and salt.
Pour in mushroom broth, balsamic vinegar, black pepper, and remaining ½ teaspoon salt. Stir everything together, scraping up any bits from the bottom of the pan.
Bring to a simmer, reduce heat to low, cover, and cook for 15 minutes, stirring occasionally. Uncover and simmer another 5 - 10 minutes until the sauce is thick and glossy. Stir in brown sugar, if using, to mellow acidity.