Finely chop the shallots. In a saucepan, melt the butter over low heat. Add the shallots and sauté until translucent, about 3-5 minutes.
Pour in the white wine and bring to a simmer. Reduce the heat to medium and let the wine reduce by half, about 5 minutes.
Add the heavy cream, salt, white pepper, and thyme sprig. Stir well to combine. Reduce the heat to low and simmer for 5-7 minutes, or until the sauce has thickened slightly.
Remove the thyme sprig. Stir the sauce and taste. Adjust seasoning with additional salt and pepper, if needed.
Serve the sauce hot over grilled fish, chicken, or vegetables.
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