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Finely chop one half of the onion.
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Slice the remaining half and set aside.
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In a large bowl, combine the chopped onion, egg, bread crumbs, 1 tablespoon water, thyme, salt, pepper and half of the garlic, then mix in the beef.
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Shape into 8 1/2" thick patties.
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In a large skillet, heat the oil over medium heat and fry the patties until browned on both sides, no longer pink inside and a meat thermometer inserted into the centre registers 160 degrees F, about 10 minutes.
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Transfer to a plate.
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Drain the fat from the pan.
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Fry the mushrooms, sliced onion and remaining garlic until the mushrooms are softened and browned, 4 minutes.
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Add the flour and cook, stirring, for 1 minute.
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Add the broth and Worcestershire sauce.
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Bring to a boil and boil, stirring, until thickened, about 2 minutes.
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Return the patties to the pan and add the parsley.
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Heat through.