In a small bowl, combine the shallot and garlic with the salt and pepper then allow to macerate for 15-20 minutes. Add the mushrooms, vinegar and thyme, and place the mixture in a food processor.
Process the mixture, drizzling in some of the vegetable broth until you get a smooth puree. You may not need all of it.
Finally, drizzle in the oil, still processing all the while.
When all the oil has been added, double check the seasoning and adjust as needed, then transfer to an airtight container (a mason jar works great for vinaigrettes) and reserve until needed.
Spoon it on a piece of grilled chicken, pork, or fish. You can also keep it in the fridge to show your friends as a conversation piece, so they can see just how much of a mushroom loving weirdo you are.