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.