Peel and thinly slice the onions. Peel and finely chop or grate the garlic.
In a medium skillet, melt the butter with the olive oil over medium heat.
Add the sliced onions and cook over low heat for 15-20 minutes, stirring frequently, until they are golden brown and caramelized.
Sprinkle the brown sugar over the onions, then pour in the wine vinegar and stir to combine. Let it simmer for 1-2 minutes to mellow the vinegar.
Add the chopped garlic and cook for another 1-2 minutes, until fragrant.
Pour in the heavy cream, stir well, and cook over low heat for an additional 3-4 minutes, until the sauce thickens to a creamy consistency.
Season with salt and pepper to taste, then remove from the heat and let it rest for a few minutes.
For a smoother sauce, purée with an immersion blender. Alternatively, leave it rustic and chunky.
Serve warm with meats, pasta, or vegetables. It can be stored in an airtight container in the refrigerator for 3-4 days.
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