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Heat thick-bottomed pot over low heat. Add olive oil and butter and melt.
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Add mushrooms and onions, stir with wooden spoon and sweat until soft. (Note: It may seem like there is a lot of fat in the pot but the mushrooms will absorb it, and release water as well. This is needed for thickening the gravy.)
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Add garlic, cook briefly and stir in dried thyme.
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Add flour and mix until it soaks up liquid and forms paste-like consistency known as roux.
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When roux is formed and hot, add ⅓ of the cold broth and stir quickly and well until combined.
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Turn up heat under pot and stir in another ⅓ of broth. Stir well until combined.
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Stir in last of the broth and combine well.
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Whisk in fresh thyme, pepper and tamari. Taste and adjust seasonings. (Note: If gravy is not thick enough, continue to simmer. If gravy is too thick, add more mushroom broth.)