Melt 1/4 cup butter in a large skillet over medium-high heat; add mushrooms, and sauté 12 to 14 minutes or until liquid evaporates. Add chives, and sauté 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 dry mustard. Gradually whisk in milk and next 3 ingredients; cook, whisking constantly, until mixture is thickened and bubbly. Stir in mushroom mixture, and cook until thoroughly heated.
*3 tablespoons chopped green onions may be substituted.