Finely chop the red onion, garlic, and fresh tarragon. If the capers are large, chop them into smaller pieces as well.
In a medium saucepan, heat the olive oil over medium heat. Add the chopped red onion and garlic and sauté for 2-3 minutes, or until translucent.
Add the red wine, apple cider vinegar, and brown sugar. Simmer over medium heat for 5-7 minutes, or until the sauce has slightly reduced and thickened.
Add the capers and chopped tarragon, and stir to combine. Reduce the heat to low and simmer for another 5 minutes.
Remove from heat and stir in the butter until the sauce is silky smooth. Season with salt and black pepper to taste.
Let the sauce cool slightly before serving over roasted meats, grilled fish, or steamed vegetables. It can be stored in the refrigerator for up to 3-4 days.
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