Melt the butter in another medium saucepan. Add the onion and cook over moderately high heat, stirring occasionally, until softened, about 3 minutes. Add the sliced cremini and cook until tender and their liquid has evaporated, about 5 minutes. Season the cremini with salt and white pepper and stir in the flour. Strain the stock into the saucepan, pressing hard on the solids with the back of a spoon. Stir the soy sauce into the mushroom soup, cover partially, and simmer until slightly thickened, about 10 minutes.