In a large cast-iron skillet, heat the oil over medium heat. Add the mushrooms, salt, and pepper and toss to coat. Let the mushrooms cook, without stirring, for 2 to 3 minutes. This will help them get a nice golden brown sear.

Give the pan a good shake or two and continue cooking the mushrooms, stirring only occasionally, until soft and well-browned, 5 to 8 more minutes depending on the size of your mushrooms. Turn the heat to low and stir in the rice vinegar, tamari, and garlic. Turn off the heat and sprinkle with fresh tarragon. Serve hot.