Slice the onions thinly.
In a medium saucepan, melt the butter over medium heat, then add the onions.
Sauté the onions for 10-15 minutes, until softened and caramelized, stirring occasionally.
Sprinkle the brown sugar over the onions and sauté for another 2-3 minutes, allowing the onions to develop a deep, sweet flavor.
Pour in the red wine and bring to a simmer. Let it simmer for about 5 minutes to allow the alcohol to evaporate.
Add the broth, balsamic vinegar, fresh thyme, salt, and pepper.
Simmer over medium heat for 15-20 minutes, allowing the sauce to thicken and the flavors to meld.
If you prefer a thicker sauce, whisk the cornstarch with cold water and add it to the sauce. Cook for another 2-3 minutes, until it reaches the desired consistency.
Before serving, strain the sauce for a smoother texture, if desired. Serve warm with roasted meats or vegetables.
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