Heat the olive oil in a large skillet over medium heat. Add the shallot and cook until soft, about 4 minutes.

Add the mushrooms and cook until soft, about 8 to 10 minutes. Stir in the tamari, garlic, thyme, and rosemary. Sprinkle the flour over the mushrooms and stir for 1 minute.

Add the broth and simmer until thickened, whisking often, about 20 minutes. Season with salt and pepper to taste.