Don't let the name fool you. The flavor of this sauce is subtle--not oniony at all.
Melt butter in a medium saucepan over medium heat; add onion, and sauté 5 to 7 minutes or until lightly browned. Whisk in flour. Cook, whisking constantly, until lightly browned (about 1 minute). Gradually whisk in broth and next 2 ingredients. Cook, whisking constantly, until thickened and bubbly. Garnish, if desired.
Mushroom-Onion Sauce: Melt 1 tablespoon butter in a large nonstick skillet over medium-high heat. Add 1 (8-ounce) package sliced fresh mushrooms, and sauté 10 minutes or until browned. Remove from heat. Prepare Onion Sauce as directed; stir in mushrooms, and cook, stirring constantly, until thoroughly heated. Makes about 2 1/2 cups. Prep: 10 min., Cook: 20 min.
Beef-Onion Sauce: Prepare Onion Sauce as directed, substituting 1 (14-ounce) can beef broth for chicken broth. Makes about 1 1/2 cups. Prep: 10 min., Cook: 10 min.