Heat the olive oil in a medium saucepan over medium heat. Add the onions and mushrooms and cook until softened and caramelized, 8–10 minutes.
Sprinkle the flour and thyme over the mushroom mixture and stir until the flour is incorporated and the thyme is fragrant, about 1 minute.
Add the broth and soy sauce and simmer until the sauce thickens, whisking occasionally, about 10–15 minutes. Taste and season with salt and pepper. Remove it from the heat and serve.
Video
Notes
Storage: Store leftovers in an airtight container in the fridge for up to 5 days.