Combine the bread crumbs, 1/8 cup Parmigiano Reggiano, salt and pepper on a plate and mix together.
Wash scallops and remove the small, tough side muscle. The side-muscle is a little rectangular tag of tissue on the side of the scallop. It feels tougher than the rest of the scallop and its muscle fibers run opposite the fibers in the scallop itself. Just pinch it between your thumb and first-finger with a paper towel, and tear it away.
Pat the scallops very dry with paper towels and place them in a small bowl.
Add 1 Tablespoon olive oil and mix to coat.
Dip the scallops in the bread crumb and cheese coating, turning to cover evenly.
Gently press the crumbs onto the scallops.
Place the scallops in a single layer on a clean plate.
Cover with plastic wrap and refrigerate for 30 minutes to set the crumbs.
For the cheesy polenta:
While the scallops chill, pour the chicken broth into a medium saucepan and place over high heat.
Season the broth with salt and pepper, and then bring to a boil.
While whisking, slowly pour the polenta into the broth a little at a time. Be sure not to add too much of the Polenta too soon or it will cause lumps.
Reduce the heat to medium-low and simmer the polenta for 20 minutes, stirring frequently.
Stir in 1/4 cup Parmigiano Reggiano, butter, and more salt and pepper, if needed.
For the lemon garnish (Optional):
Finely chop the parsley and lemon zest and mix together. Add the olive oil and lemon juice.
For the grill:
Spray a grill grate generously with olive oil.
Place the scallops on the grill grate 1 - 2 inches apart and grill over direct medium heat until just opaque in the center, about 5 - 8 minutes, turning once halfway through grilling time. Treat them gently when turning.
Remove from the grill.
Spoon half the polenta onto each plate, top with the scallops.
(Optional) Drizzle some of the garnish onto each scallop and serve warm.
If you don’t want to use the lemon garnish you can also just drizzle some olive oil onto each scallop.
Video
Notes
If you don’t want to use the lemon garnish you can also just drizzle some olive oil onto each scallop.
Don't worry too much if you can't find all the side muscles. They often get dislodged and washed away during the harvesting process and won't harm your dish if a few slip through.