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1
Bring 1 inch of water to a boil in a large covered pot. Plunge the lobster into the pot, cover, allow water to return to a boil, and cook for 8 to 10 minutes.
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2
Remove the lobster, and let it sit until cool enough to handle. Remove the meat from the shells.
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3
Melt the butter in a medium saucepan over low heat, then add the champagne, and simmer for 1 minute.
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4
Turn off the heat, add the lobster, and let it sit while you prepare the rest of the meal.
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5
To prepare the hollandaise sauce, melt the butter in a small saucepan over low heat or in the microwave. Do not let it brown.
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6
Combine the egg yolks, lemon juice, salt, and dry mustard or cayenne pinch in a blender. Pulse and drizzle in the butter. The mixture will begin to thicken. If the sauce is too thick, add a few drops of warm water. Taste and adjust the seasoning . Transfer the sauce to a container nesting in ab olw of hot water to keep it warm while you continue.
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7
Toast the English muffins, and keep them warm.
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8
To poach the eggs, heat 2 to 3 inches of water in a deep, small skillet until almost boiling. Add the vinegar and salt. Crack the eggs into 2 smalls cups and carefully slide on at a time into the simmering water. Reduce the heat if necessary, to keep the water just below a simmer. At this point, cover the pan or begin to spoon water over the tops of the eggs. cook for 3 to 5 minutes, just until the white is set and the yolk has filmed over. Remove the eggs with a slotted spoon and press against a paper towel to drain any excess water.
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9
To assemble, place each English muffin half on a plate. Then, top with arugula, lobester meat, and then a poached egg. Top each half with 4 tbs of the hollandaise, and serve immediately. if you're inclined, garnish with Ossetra or Servuga caviar, or simple chives.
