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For Sauce Base:
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Combine Champagne, shallots, vinegar, and peppercorns in heavy medium saucepan.
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Boil until reduced to 1/4 cup liquid, about 20 minutes.
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(Can be made 4 hours ahead. Cover and let stand at room temperature.)
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For Shrimp:
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Combine Champagne, olive oil, shallots, and ground pepper in resealable plastic bag.
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Add shrimp to bag and seal; shake bag to coat shrimp evenly.
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Marinate shrimp at room temperature at least 30 minutes and up to 1 hour, turning bag occasionally.
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Mix chives, tarragon, and parsley in small bowl.
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Preheat broiler.
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Spray broiler pan with nonstick vegetable oil spray. Drain shrimp; discard plastic bag with marinade.
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Arrange shrimp on prepared pan in single layer.
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Broil shrimp until just opaque in center, about 2 minutes per side.
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Stand 3 shrimp, tails upright, in center of each plate.
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Rewarm sauce base over medium-low heat. Whisk in butter 1 piece at a time, just allowing each to melt before adding next (do not boil or sauce will separate).
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Season beurre blanc to taste with salt and pepper.
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Spoon warm sauce around shrimp.
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Sprinkle with fresh herbs and serve.
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Market tip: Champagne and sparkling wines labeled extra dry are actually slightly sweeter than those labeled brut. The latter works best for this dish.
