Sprinkle steaks on both sides with 1/8 teaspoon each salt and black pepper. Sprinkle scallops on both sides with 1/8 teaspoon each salt and pink peppercorns.
Heat 1 1/2 teaspoons oil in a large cast iron or heavy-bottom nonstick skillet over medium-high heat. Add steaks, and cook 3 minutes on each side (for medium-rare) or until desired degree of doneness. Transfer to a platter; cover and keep warm.
Add remaining 1 1/2 teaspoons oil to skillet; add scallops, and cook 2 minutes on each side or until done. Transfer to platter; cover and keep warm.
Add Champagne, lemon juice, and shallots to pan; bring to a boil. Cook 3 minutes or until reduced to 2 tablespoons. Remove from heat. Add butter, 1 piece at a time, whisking constantly until butter is thoroughly incorporated. Season sauce to taste with salt and black pepper. Top steak and scallops with sauce.
This was our Valentine's Day dinner and it was delicious. Simple yet elegant. I found that I had to watch the steaks--3 minutes on each side just barely got them to "rare," but then I may've slightly overcooked them ( our preference medium rare) with 2 to 3 additional minutes on each side. The scallops were perfect, and the sauce was fine. I used more liquid (both lemon juice and champagne) and shallots than the recipe called for, and slightly less butter. Will try this again for sure (when filets and scallops are on sale!).