In a large skillet, melt the butter in the olive oil. Add the mushrooms and cook over moderately high heat, without stirring, until browned on the bottom, about 3 minutes. Continue to cook, stirring occasionally, until the mushrooms are browned and tender, about 6 minutes longer. Add the garlic and cook until fragrant, about 1 minute. Stir in tarragon and season the mushrooms with salt and pepper. Transfer to a bowl and serve.