Wash the wild mushrooms and cut them into smaller pieces if needed. (Cut off any dirty ends.)
Peel and dice the shallot and peel and mince the garlic cloves.
Heat the olive oil in a large skillet over medium-low heat. Add the shallot and garlic then cook until soft, about 4-5 minutes.
Add the mushrooms and cook until soft, about 6-8 minutes. Sprinkle the flour over the mushrooms and stir for 1 minute.
Slowly add the broth and stir well until there are no lumps. Stir in the tamari, thyme, and rosemary then simmer until thickened, whisking often, about 15 minutes. Season with salt and pepper to taste.
Notes
Add the liquid to the roux slowly being sure to stir well between each scoop.
Make sure to stir constantly during the thickening process.
To make gluten-free mushroom gravy*Omit the step of adding the flour, then along with the broth, add a slurry made of 2 tablespoons of cornstarch (or potato starch) and 1/4 cup of cold water. (Be sure the starch is fully dissolved in the water before adding to the gravy.) Heat until it bubbles and thickens. Also, be sure to use Tamari or Bragg's Liquid Aminos instead of soy sauce to make it gluten-free.