Put 4 tablespoons butter in skillet over medium-high heat. When foam subsides, add scallops; sprinkle with salt and pepper. Brown on both sides, adjusting heat so they brown nicely; they need not cook through. Remove them to a plate.
Turn off heat, cool pan a bit and wipe out. Add remaining 2 tablespoons butter over medium heat. When it melts, add shallots, garlic, chile flakes and a little more salt and pepper. Cook about 2 minutes, or until shallots soften.
Add wine, raise heat a bit, and let bubble away for a minute or so until reduced by about 1/2; add cream and repeat. When liquid is thick, return scallops and juices to pan.
Cook for about a minute, stirring in 1/2 the basil, until scallops are just firm. Taste and adjust seasoning, transfer to small bowls or plates with a bit of sauce, garnish with remaining basil, and serve.