Wipe the mushrooms clean with a damp cloth. Slice 1/4 inch thick. Set aside.
Heat olive oil in a large skillet and add the onion and garlic. Saute until the onion is softened and the garlic is fragrant, 3-4 minutes.
Add the vinegar, brown sugar, lemon pepper and tarragon. Simmer mixture for a few minutes. Add the mushrooms and continue to cook 7-10 minutes, stirring frequently. The liquid should reduce and thicken slightly.
Put in a glass jar or zip top bag and refrigerate overnight or for up to 3 days. Serve as part of a relish tray, on a salad, or as a side dish.