Place broth and water in a small pot and bring to a simmer, then stir in miso until disolved.
At the same time, heat butter ( or oil) in a large skillet and saute mushrooms and shallot over med-high heat. Saute 7-8 minutes, lowering heat if necessary, stirring occasionally, until mushrooms have fully released their liquid and all this liquid has cooked off.
Lower heat to medium, add garlic and thyme, saute 2 minutes.
Sprinkle the flour over top and stir to combine, cooking and stirring the flour 2 minutes, letting it brown a bit. Here is where the flavor is!
Add 1/2 of the hot broth, whisking and scraping all those flavorful browned-bits. When incorporated, add the remaining broth, stirring to combine Simmer gently on med-low until reduced and thickened, about 5 minutes. Taste for salt, adding some if needed along with pepper.