Using a damp paper towel or a clean sponge, gently wipe the mushrooms to remove any dirt. Avoid rinsing them under water, as mushrooms absorb moisture, which can hinder proper browning. Slice them into ½-inch-thick pieces for even cooking.
Heat a large skillet or Dutch oven over medium heat and add the olive oil. Once the oil is shimmering, add the butter and let it melt completely. Stir in the sliced mushrooms, followed by the salt and freshly ground black pepper. Sauté, stirring occasionally, until the mushrooms become tender and release their natural juices. Continue cooking until most of the liquid has evaporated, about 8 to 10 minutes. If excessive moisture collects in the pan, drain it off to expedite the process.
Pour in the soy sauce and balsamic vinegar, stirring well to coat the mushrooms. Add the minced garlic and cook for an additional 30 seconds, stirring continuously to prevent it from burning.
Remove the skillet from heat and fold in the fresh thyme or parsley. Taste and adjust seasoning if needed, adding an extra splash of balsamic vinegar for more depth. Serve warm, garnished with additional fresh herbs for a vibrant finish.