Finely mince the garlic and fresh tarragon. Measure out all the ingredients so they are easily accessible during cooking.
In a medium saucepan, heat the olive oil over medium heat. Add the minced garlic and sauté for 1-2 minutes until fragrant, being careful not to burn it.
Pour in the red wine and white wine vinegar, then stir in the brown sugar. Cook over medium heat for 5-7 minutes, or until the liquid has slightly reduced and thickened.
Add the chopped tarragon, then reduce the heat to low and stir in the butter. Continue stirring until the sauce is smooth and silky.
Season with salt and black pepper to taste. For a more intense flavor, add a little more tarragon or vinegar.
Let the sauce cool slightly before serving with roasted meats, grilled vegetables, or pasta. It can be stored in the refrigerator for up to 3-4 days.
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