Preheat the oven to 425°F and place the oven rack about 10 inches from the top heating element.
Rinse the sea scallops to remove any debris or ice particles and pat dry with a paper towel.
Melt butter in the microwave (or on the stovetop) and combine it with olive oil.
In a second shallow bowl combine breadcrumbs, grated parmesan cheese, chopped parsley, paprika, and black pepper.
Lightly brush each scallop with the butter mixture, allowing excess butter to drip off.
Roll each scallop in the parmesan breading, shaking off excess crumbs, and place it on a broiler pan coated with cooking spray. Note: If you have a grill rack or cookie cooling rack that fits over a shallow baking pan, use it. This will help the bottoms of the scallops to crisp and not get soggy. Alternatively, you can skip breading the bottom of the scallops.
Broil the scallops for 10 minutes or until they are moist and white in the center and the tops are golden brown.The exact timing will vary depending on the oven, the size of the scallops, and how heavily they are breaded. They cook very quickly, so keep an eye on them, opening the oven door if you have to in order to get a good look at the progress.
Notes
To make ahead and freeze, prepare scallops through breading step. Freeze in a single layer in a tin, cover and wrap with plastic wrap. Defrost overnight and then cook according to instructions.