Place sea scallops on a paper towel. Place a second paper towel on top, pressing very gently on top of the scallops.
Bring a large pot of water to a rapid boil, then season. Cook pasta according to package directions.
Season scallops and shrimp on both sides with salt and pepper. When hot, add scallops to the pan and cook.
Cut 1 lemon into thin slices. Add lemon to the pan, then cook until charred. Remove to the tray with seafood.
Add another 2 Tbsp each of olive oil and unsalted butter, then add minced garlic, anchovies, lemon zest, and red pepper flakes. Cook. Pour in the drained, cooked pasta. Stir.
Add seafood and cooked lemon slices back to the skillet, stir in freshly grated Parmesan cheese and chopped fresh parsley.