Melt 1/4 cup butter in a in a large skillet over medium-hgh heat; add mushrooms and saute 15 minutes or until liquid evaporates. Add green onions and saut additional 2 minutes. Remove from heat.
Melt remaining 1/4 cup butter in a large saucepan over medium heat; whisk in flour until smooth. Cook, whisking constantly, 1 minute. Whisk in Dijon mustard. Gradually whisk in beef broth and wine. Whisk in salt and pepper. Cook, whisking constantly, until mixture is thickened and bubbly. Stir in mushroom mixture and cook until thoroughly heated.