Melt butter in a separate skillet over medium-high heat. Saute mushrooms and onion in melted butter until tender, 5 to 7 minutes. Stir flour and remaining dry onion soup mix into the mushroom mixture; cook and stir until flour is integrated fully, about 1 minute. Stream beef stock and water over the mushroom mixture while stirring continually; bring to a simmer, reduce heat to medium, and cook, stirring frequently, until the liquid thickens, about 5 minutes. Season with salt and pepper.