Finely dice the shallot and finely chop the fresh tarragon.
In a small saucepan, heat the white wine over medium heat and add the diced shallots.
Simmer until the liquid is reduced by about half to intensify the flavor.
Add the heavy cream and cook for another 2-3 minutes, or until slightly thickened.
Remove from the heat and gradually whisk in the cold butter cubes, one at a time, until you achieve a smooth, creamy consistency.
Stir in the lime juice and lime zest, then season with salt and white pepper to taste.
Finally, add the chopped tarragon and mix well.
Strain the sauce through a fine-mesh sieve for a smooth and silky texture.
Serve warm with fish, roasted chicken, or as an accompaniment to steamed vegetables.
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