Steak and eggs is for Sundays when you want to feel powerful before noon. Add hollandaise and it becomes a low carb brunch that means business.
Season both sides of the ribeye steak generously with 3/4 tsp kosher salt and 1/4 tsp black pepper; let sit at room temperature for 15 minutes while you prepare the hollandaise.
For the hollandaise: In a small heatproof bowl, whisk together 2 egg yolks, lemon juice, Dijon, and water. Place bowl over a barely simmering saucepan (double boiler); whisk constantly, ensuring the heat stays low to prevent scrambling eggs.
Slowly drizzle in the melted butter, whisking vigorously until the sauce thickens and becomes glossy. Remove from heat, season with 1/4 tsp salt and a pinch of pepper, and keep the sauce warm (not hot).
Heat a heavy skillet over medium-high heat. Add 1 tbsp butter and, once foaming, lay in the steak. Sear undisturbed for 3-4 minutes, flip, and cook until desired doneness (125°F for medium-rare), basting with pan drippings. Rest steak under foil for 5 minutes.
Wipe out skillet, reduce to low-medium heat, and add 1 tbsp butter. Crack in eggs and fry sunny-side up, basting with butter and covering briefly to set the whites without overcooking. Sprinkle with remaining salt and pepper.
Slice steak against the grain. Plate with two eggs per serving, spoon warm hollandaise over the eggs, and serve immediately.