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1
Combine white wine, vinegar, shallots, and thyme in a heavy-bottomed saucepan over medium-high heat.
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2
Reduce until approximately 30 ml of liquid remains and the shallots are just visible at the bottom (6–8 minutes); the reduction should be glossy and syrupy.
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3
Remove from heat, discard thyme, and let cool to 50°C for 1 minute.
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4
Return to very low heat and whisk in cold butter cube by cube, adding each piece only after the previous one is half-incorporated; never allow the sauce to exceed 55°C or the emulsion will break.
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5
Once all butter is incorporated, pass through a fine-mesh sieve into a clean, warm pot.
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6
Season with salt, white pepper, and lemon juice if desired.
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7
Hold in a warm water bath at 43–50°C; stir gently every 2 minutes and never allow temperature to exceed 55°C.