How to Make It
Melt 1⁄4 cup of the butter in a large saucepan over medium. Whisk in flour; cook, whisking constantly, until mixture is the color of caramel, 5 to 6 minutes.
Gradually whisk in stock, salt, and pepper. Cook, stirring often, until heated through and smooth, 3 to 4 minutes. Keep warm over low heat until ready to use, up to 30 minutes. (This base sauce can be refrigerated or frozen for later use.)
Melt remaining 3 tablespoons butter in a heavy skillet over medium-low. Add onions. Cook, stirring constantly, until rich brown, 30 to 40 minutes.
Stir in wine and vinegar. Bring to a boil; cook until liquid has almost evaporated, about 3 minutes. Add warm base sauce to onion-and-vinegar mixture; bring to a boil. Cook until hot and bubbly, about 5 minutes. Sprinkle with additional salt and pepper to taste.