Melt butter in a skillet; add mushrooms and garlic, and saut until tender.
Remove mushrooms with a slotted spoon, reserving drippings in skillet.
Whisk flour into reserved drippings until smooth. Cook, whisking constantly, until lightly browned. Gradually add wine and broth; cook over medium heat, whisking constantly, until thickened and bubbly. Stir in salt and pepper.
Add mushrooms; cook, stirring constantly, until sauce is thoroughly heated.