Heat a large cast-iron skillet over medium heat and add 2 tablespoons extra-virgin olive oil; heat until the oil shimmers.
Add 16 ounces mixed mushrooms (sliced or chopped), a heaping ¼ teaspoon sea salt, and freshly ground black pepper (to taste). Toss to coat the mushrooms in the oil and seasonings.
Let the mushrooms cook without stirring for 2 to 3 minutes to develop a golden-brown sear.
Give the pan a good shake, then continue cooking over medium heat, stirring only occasionally, until the mushrooms are soft and well-browned, about 5 to 8 minutes more (depending on mushroom size).
Reduce the heat to low and stir in 1 tablespoon rice vinegar, 1 tablespoon tamari, and 1 garlic clove (minced or grated).
Turn off the heat, sprinkle with 1 tablespoon finely chopped fresh tarragon, and serve hot.