Remove steaks from the refrigerator; allow them to come to room temperature—about 15 to 20 minutes.
Brush the steaks with olive oil and rub with coarse kosher or sea salt and freshly ground pepper.
Heat a frying pan or grill pan over medium-high heat. Sear the steaks for 1 to 2 minutes on each side. Transfer steaks to plates and let rest.
Heat 1 tablespoon of regular butter in frying pan.
Combine eggs, milk, paprika, and seasoning in bowl; beat well.
Add desired amount of sausage to pan and brown. Remove from pan and set aside.
Add remaining tablespoon of butter to pan.
Add eggs to pan and stir to scramble. When eggs are nearly firm, add green onion and brown sausage. Stir to combine until eggs are desired consistency. Salt and pepper to taste.