Remove the beef from pan with a pair of tongs or a slotted spoon. Strain the contents of the Dutch oven through a China cap or fine mesh colander into the large dish. Return the velvety sauce and the beef to the Dutch oven. Bring the Bourguignonne up to a simmer. Adjust the seasonings.
Slice the onions into large wedges. Clean and quarter the mushrooms. To make the garnish, heat a 12 inch iron or aluminum skillet over a medium flame. Melt the butter, add the mushrooms, and saute until there is sufficient color on them. Add onions to the pan, and heat through. Do not attempt to brown the onions. The onions must retain a firmness in order to contribute to the texture of the Bourguignonne. Stir the mushrooms and onions in to the re-simmering contents of the Dutch oven. De-glaze the skillet with wine; Add the de-glazing liquid to the Dutch oven. Allow the ingredients to come up to a simmer, then cut off heat. Serve with crusty, French bread.