Preheat oven to 400°F. Coat a baking sheet with cooking spray.rrange the polenta on the prepared baking sheet and bake until crispy on the bottom and heated through, about 20 minutes.
Meanwhile, heat oil in a large skillet over medium-high heat. Add onion and cook, stirring often, until lightly browned, 2 to 3 minutes. Stir in mushrooms, salt and pepper, and cook, stirring often, until the mushrooms are softened and most of the liquid has evaporated, 8 to 10 minutes.
Pour in wine; bring to a boil and scrape up any browned bits from the bottom of the pan. Reduce the liquid until the pan is almost dry, 2 to 3 minutes. Stir in sour cream and bring to a simmer. Remove from the heat, stir in cheese and tarragon. Serve the sauce over the polenta.