Peel and thinly slice the red onions to ensure they caramelize quickly.
In a medium saucepan, melt the butter over low heat, then add the onions. Sauté until they are a deep golden brown and caramelized, about 15 minutes.
Sprinkle the brown sugar over the onions and stir to coat, enhancing their sweetness and adding a glossy finish.
Pour in the red wine and bring to a simmer. Allow the alcohol to evaporate for about 5 minutes.
Add the beef broth and balsamic vinegar, then reduce the heat to low and simmer for another 10-15 minutes, or until the sauce has thickened to your liking.
Season with salt and freshly ground black pepper, then stir to combine. For a smoother sauce, use an immersion blender to purée until smooth.
Serve immediately over steak, roasted meats, or grilled vegetables, or store in an airtight container in the refrigerator.
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