Add a splash of the beef broth to the pan, scraping and stirring the beef drippings - this is called deglazing.
Once the beef is all scraped off the bottom of the pan and incorporated, add red wine vinegar and tomato paste, stir well to combine. Add remaining beef broth, bay leaves, and the beef.
Bring to a boil, then reduce heat to a low simmer. Simmer over low heat for 1 ½ hours, or until meat is very tender.
As the beef cooks, prepare your vegetables: Quarter or slice the mushrooms, chop the onion, peel and slice the carrot, chop the celery, press or mince the garlic.
Add all of the vegetables to the pot, stir to combine.
Bring it to a boil again, then turn heat back down to low and simmer for another 30 minutes or so, until the vegetables are tender.
As the vegetables are boiling, drain the kidneys, rinse with cool water. Pat dry with paper towels, season with salt and pepper.
Add a little vegetable oil to a nonstick pan, and brown the kidneys over medium high heat - this should only take a couple of minutes. When browned all over, remove from heat, set aside.
In a small bowl, combine the dried parsley, gelatin, xanthan gum, and dried thyme. Be sure to stir well - you want the xanthan gum well distributed over the other ingredients, to prevent clumping.
Add herb mixture to the pot, stir well to combine. Add the browned kidney meat, stir again to combine.
Allow stew to simmer for a 5 minutes, to thicken the stew and cook the kidneys through.
Remove the bay leaves. Taste, season with salt and pepper, and serve.