Add 1 tablespoon olive oil to a hot pan. Add chopped onion and cook on low heat for about 35 minutes, or until onions are caramelized. Add balsamic vinegar to deglaze the pan. Add salt.
Add sliced mushrooms and the rest of olive oil. Cook about 5 minutes, or until tender. Add salt and pepper.
Add gluten free flour. Cook 2 minutes. Add vegetable broth and tamari. Bring to a boil. Reduce heat and simmer about 5 minutes to thicken.
Take ½ the cooked mushrooms and onions and blend in a food processor. Add back to gravy.