Season steaks on all sides with salt and pepper right before cooking. Brush grill pan or cast iron pan with oil and heat over medium-high heat. Put 1 to 2 pieces steak on the pan and cook for 4 to 6 minutes on each side, longer if desired. Remove steaks and let rest for 5 to 10 minutes before serving. Repeat with the remaining steaks.
Make the creamy eggs: Whisk eggs together with milk, salt, and pepper in a bowl until well combined.
Melt butter in a small nonstick skillet over medium-low heat. Pour in egg mixture and gently stir with a heatproof rubber spatula. Continue cooking, stirring occasionally, until the eggs have set but still remain soft and creamy. Sprinkle parsley on top.
Make the hash browns: Melt butter in a large sauté pan. Add potatoes, garlic, salt, and pepper. Cook over medium-low heat for 15 to 20 minutes, turning occasionally with a flat spatula, until the potatoes are evenly browned and cooked through. (Allow the potatoes to cook for 5 minutes before turning for the first time.) Turn off heat..
To assemble, arrange steaks on individual platters. Put equal portions of creamy eggs and hash browns on the side of each plate.