Move an oven rack to the top of your oven, and turn on the broiler.
Set scallops in the ramekins, on top of the mushroom and shallot mixture.
Pour the pumpkin sauce into the ramekins, covering the SIDES of the scallops, but not the tops.
Divide the Parmesan on top of both ramekins.
Set ramekins on a baking sheet, and then slide it onto the top oven rack under the hot broiler.
Broil the scallops for 5-7 minutes until the cheese has turned golden and is bubbling. (Watch the scallops carefully after about 5 minutes– you want them golden, not burnt.)
Allow the ramekins to cool slightly, top with fresh chives (if desired) and serve your broiled scallop gratin while it’s still hot.