Melt the remaining 4 tablespoons of butter in the pot. Once bubbly, add the flour and whisk to incorporate it into the butter. Continue stirring until the flour takes on a nutty aroma, about 2 minutes.
Whisking regularly, pour in the vegetable stock, and continue whisking until a slurry forms. Next, begin adding the heavy cream in half cup increments and whisking after each addition. Continue until all of the cream has been added, and the sauce is thick. Season with salt.
Simmer for 5–10 minutes over low heat until the sauce is thickened to your liking. Season it with salt, white pepper, and nutmeg.
Fold the cooked mushrooms and onions into the sauce and stir to coat. Turn off the heat and set it aside.