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While eggs are simmering, cook bacon in a 10-inch heavy skillet over moderate heat, stirring, until crisp, about 8 minutes. Transfer bacon with a slotted spoon to paper towels to drain, leaving rendered fat in skillet.
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Peel eggs and finely chop.
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Put romaine and egg in a serving bowl.
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Add oil and shallot to fat in skillet and cook over moderate heat, stirring, until shallot is softened, about 2 minutes. Add vinegar and salt and boil, swirling skillet, 10 seconds. Pour hot dressing over romaine and egg and toss to combine. Add bacon and toss salad, then season with salt and pepper.