This festive first course features a buttery scallop and an earthy potato and squash puree.
Heat oven to 425 degrees. Place the potato and the butternut-squash chunks in a large stockpot. Cover the vegetables with cold salted water; bring to a boil. Reduce heat to medium high; simmer until vegetables are tender, about 15 minutes. Drain vegetables in a colander. Pass through the fine holes of a food mill set over a large metal bowl. Set the vegetable puree aside.
Have ready a pan of gently simmering water. In a small saucepan, combine 3 tablespoons butter and the cream; cook over medium heat until the butter has melted and the cream is hot, about 3 minutes. Pour the cream mixture into the reserved vegetable puree. Add the snipped chives, and season with salt and pepper; mix until combined. Place bowl of puree, covered, over the simmering water.
Trim the bacon slices so they are as wide as the scallops are thick. Wrap each scallop in bacon, trimming bacon so that it overlaps by about 1/4 inch; secure with kitchen twine. Season the scallop surfaces with salt and pepper.
Heat the olive oil in a large ovenproof skillet set over high heat. Place scallops in the skillet, with bacon down, and cook, turning, until the bacon is well browned all around, 4 to 6 minutes. Turn each scallop so one of the exposed scallop surfaces faces down, and cook until bottom is deep brown, about 1 minute.
Flip the scallops over, and transfer the skillet to the oven. Cook the scallops until they are opaque, about 2 minutes. Remove the skillet from oven. Transfer scallops to a warm place.
Pour off all the bacon fat from the skillet. Pour the vinegar and the chicken stock into the skillet. Using a wooden spoon, scrape up any brown bits from the bottom. Set the skillet over medium-high heat, and cook until the liquid has reduced by half, 1 to 2 minutes. Add the remaining tablespoon butter, and swirl in the skillet until the sauce has thickened and the butter has melted, 1 to 2 minutes. Pass the sauce through a fine sieve set over a bowl, and set the sauce aside in a warm place.
When ready to serve, use a pair of kitchen shears to carefully snip and discard kitchen twine from the scallops. Divide the warm puree among twelve plates, and garnish with snipped chives. Place a scallop on each bed of puree, and drizzle with the reserved sauce.