Heat 1 tablespoon of the olive oil in a wide skillet or Dutch oven over medium-high heat. Add the chopped mushrooms in a single layer and let them sit undisturbed for 4 to 5 minutes, until the undersides turn golden. Stir, then keep cooking while stirring every couple of minutes, until the mushrooms release their liquid, the liquid cooks off, and the pieces are deeply browned with a crusty layer stuck to the pan, 8 to 10 minutes total.

Push the mushrooms to one side of the pan and add the remaining tablespoon of olive oil to the empty side. Add the onion and cook, stirring now and then, until it softens and the edges start to turn golden, 4 to 5 minutes. Stir in the garlic and cook for 30 seconds until fragrant, then mix everything together with the mushrooms.

Sprinkle the flour over the vegetables and stir constantly for 1 to 2 minutes, until the flour is fully absorbed and smells lightly toasted. This step cooks out the raw-flour taste before any liquid goes in, so don't rush it.

Pour in the vegetable broth in a slow, steady stream while whisking, scraping up the browned bits from the bottom of the pan as you go. Add the tamari or soy sauce, thyme, and Dijon mustard, and bring the gravy to a simmer.

Lower the heat so the gravy stays at a gentle simmer and cook, whisking now and then, until it thickens to a glossy sauce that coats the back of a spoon, 8 to 10 minutes. Taste and adjust the salt and pepper. For an ultra-smooth finish, blend it with an immersion blender or pass it through a fine strainer, though neither is required for a silky result.