Thaw the frozen scallops overnight in the refrigerator. Place the scallops in a colander in the sink and run cold water over them for 4-5 minutes until completely thawed.
Remove the side muscle from each scallop, as it will be tough. (See photo in post.) Look carefully for any specks of sand to scrape off the scallops.
Pat the scallops dry with paper towels and let them rest on a couple layers of paper towels to continue drying as you proceed with the recipe.
Move your oven rack to the top position and preheat your broiler. Line two half baking sheets with foil. Grease the foil with cooking spray.
Add your bread crumbs, Parmesan, Romano, garlic powder and pepper to a dinner plate (or use a gallon-sized, resealable plastic bag) and stir or shake to combine.
Add your butter to a microwave-safe, liquid measuring cup. Melt the butter in the microwave, covered loosely. (Try 30 seconds at first, then more as needed.)
Stir your olive oil into the melted butter in your cup.
Set up an assembly line from left to right with your scallops, butter mixture, bread crumb mixture, and foil-lined pans.
Dry your scallops again with paper towels, so you don't end up with a soggy result.
Place four scallops at a time into your butter mixture. Use a fork to turn them to coat all sides.
Transfer the scallops to your bread crumb mixture. Coat the scallops with the bread crumbs and use a different fork to transfer them to your pan. Continue breading your scallops until you've filled both pans.
Sprinkle paprika on the breaded scallops. Pour any extra butter mixture over the scallops.
Broil the scallops on the top rack (one pan at a time) for two minutes on the first side, or until browned.
Use a small metal spatula or spoon to flip over the scallops. Broil on the second side for another 90 seconds or two minutes, until browned but not burned. (Watch them carefully.)
Proceed to broil your second pan of scallops the same way. The scallops should be white and tender on the inside when cooked.
Squeeze lemon juice on the scallops before serving.
Adapted from my Mom, who uses unsalted butter and doesn't measure anything.