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1
Heat olive oil in a 2- to 3-quart heavy saucepan over medium-low heat until it shimmers, then cook onion, covered, over low heat, stirring occasionally, until wilted, about 10 minutes. Stir in 1/2 teaspoon salt and 1/4 teaspoon pepper and cook, covered, stirring occasionally, until very tender but not colored, about 20 minutes more. (If onion begins to color, add 1 to 2 tablespoons of water as necessary during cooking.)
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2
Puree onion in a blender until smooth (use caution when blending hot foods). Transfer to a bowl; keep warm, covered.
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3
Cut 1/2 inch from top and bottom of grapefruit with a sharp knife, exposing fruit at both ends. Cut peel and pith from sides, then cut segments free from membranes. Cut segments into 1/3-inch dice and reserve.
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4
Boil Prosecco and shallot in a small heavy saucepan until liquid is reduced to 1 to 2 tablespoons, about 5 minutes. Reduce heat to medium-low, then whisk in 6 tablespoons butter, 1 tablespoon at a time, whisking constantly, adding each piece before previous one has completely melted, and lifting pan from heat occasionally to cool. Remove from heat; keep warm, covered.
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5
Heat a dry 12-inch heavy skillet over medium-high heat until very hot, at least 2 minutes.
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6
Meanwhile, pat scallops dry and sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper.
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7
Add vegetable oil to hot skillet, swirling to coat, then sear scallops without crowding, undisturbed, until undersides are well browned, about 3 minutes. Add remaining 2 tablespoons butter to skillet, swirling skillet (so butter helps release scallops), then turn scallops over and cook until just cooked through, about 1 minute more.
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8
Spoon 2 tablespoons onion puree onto each of 4 plates, then top with scallops, browned sides up, and diced grapefruit. Drizzle with Prosecco butter.
