Mince the garlic or grate it very finely. Chop the fresh tarragon.
In a medium saucepan, melt the butter over medium heat.
Add the flour and whisk until combined. Cook, stirring constantly, until lightly golden brown, about 1-2 minutes.
Pour in the white wine and beef broth, whisking constantly. Cook for 2-3 minutes, until slightly reduced.
Stir in the heavy cream and Dijon mustard. Reduce heat to low and simmer for 5 minutes.
Add the green peppercorns and fresh tarragon. Cook for another 3-4 minutes, allowing the flavors to meld.
Season with salt and freshly ground black pepper. Cook for an additional 2 minutes.
Let it cool slightly before serving with roasted meats, steak, or grilled vegetables.
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