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Fill a stock pot with water and add a generous pinch of salt. Bring the water to a boil.
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Submerge the live lobsters into the boiling water and cook for 8 minutes.
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Using tongs, remove the lobsters from the water, draining any excess water. Allow to rest for 5 minutes.
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While the lobsters are cooking, start the beurre blanc: Combine the shallot, white wine and vinegar in a heavy saucepan. Cook over medium heat and reduce until all the liquid has evaporated. Add the heavy cream to this mixture, reduce heat to low and reduce by half until thickened.
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Add the butter to the sauce base, one piece at a time, whisking constantly over very low heat. Add the next cube of butter after the previous one has emulsified into the sauce.
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Watch the consistency: it should remain at a coating sauce consistency. Too thin or begins separating? Remove pan from the heat and add butter to cool. Too thick? Slow down the addition of butter or turn up the heat slightly.
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Continue in this fashion until all of the butter has been incorporated.
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Fold in the tarragon and season with salt and pepper. Keep the sauce in a warm, but not hot, place until needed.
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Cut each lobster in half lengthwise, and crack the claw in a few places to make it easier to remove the meat.
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Place the lobsters on a platter and serve with the beurre blanc.
