Place diced potatoes in a medium pot and cover with water. Bring to a boil and boil for about 10 minutes or until just fork tender.: Warm, slightly salted water should just cover the potatoes , and as they come to a simmer you will notice tiny bubbles rising from the bottom. This gentle boil helps the interiors soften so later you can crisp the outsides without waiting too long. A common trouble is dropping very cold potatoes into high heat water and then rapidly overcooking the exterior while the inside remains hard, so start with room temperature water if you can.
Drain potatoes and set aside.: Watch for the moment when a fork slides into a cube with just the right amount of resistance, indicating they are fork tender. The steam will smell faintly earthy and the texture should be soft but intact. If you boil too long the pieces will break apart in the skillet, which makes it harder to get crisp edges, so test early and often starting at around eight minutes.
Heat a large cast iron skillet over medium heat and add oil and butter.: Drain immediately and let the potatoes sit in the colander so excess steam escapes, preventing them from getting soggy. You might shake the colander gently to roughen the surfaces, which helps create more surface area for browning later. Leaving them wet will steam them in the skillet, so dryness is your friend here.
Add diced onions and slowly cook until they begin to caramelize, about 10 minutes.: As the olive oil shimmers and the butter melts into it, you will smell a faint nuttiness from the butter mixed with the oil. The combination helps raise the smoking point while maintaining flavor. If you let the pan get too hot the butter will brown and burn quickly, creating bitter notes, so keep the flame at medium and adjust as needed.
Stir in potatoes and cook until potatoes begin to brown, stirring and flipping occasionally. Season with salt and black pepper.: You want the onion to turn translucent, then golden, then seeded with darker flecks. The aroma will shift from sharp to sweet and almost nutty. Stir occasionally so they brown evenly, and lower the heat if they begin to blacken too fast. The mistake I see most is rushing this with high heat, which yields uneven, burnt pieces rather than the soft sweetness we want.
Add sliced prime rib at the end, cooking just until warmed through.: When the potatoes hit the skillet, you should hear a steady sizzle as their edges contact the hot fat. Give them space so they can brown, flipping pockets to expose new surfaces. The scent will go from buttery to toasty and the color will deepen to a warm gold. Seasoning early helps build flavor, but taste before adding more, because the prime rib will also bring saltiness.
Remove from heat, garnish with fresh chopped parsley and serve hot with sunny side up egg on top of each serving.: Slide in the thin slices of prime rib , and let the residual heat gently warm them, which preserves a tender bite and prevents drying. You may hear a softer sizzle as the meat meets the pan, and the aroma will become richly beefy. Overcooking here toughens the prime rib , so keep your contact time brief, just until warmed.
Alternatively, you can place a few wells in the hash with the bottom of a small glass and crack the eggs right into the skillet. Bake in the oven at 350° F until desired doneness is achieved (10-20 minutes). I prefer a super runny yolk, so I like to cook them separately.: The final plate should be steaming, with flecks of green parsley and a glossy egg perched on top. Breaking the yolk will create a silky sauce that threads through the hash, adding richness and cohesion. Serve immediately; letting it sit will reduce the contrast between crisp and tender.
Alternatively, you can place a few wells in the hash with the bottom of a small glass and crack the eggs right into the skillet: If you choose to bake the eggs in wells, the surface of the hash will bubble around the edges and the eggs will set while the bottoms crisp slightly. The oven method provides gentle, even heat and allows hands off finishing. A common issue is not making wells deep enough, which causes the eggs to spread and cook unevenly.
Bake in the oven at 350° F until desired doneness is achieved (10 to 20 minutes): The oven will give a soft, even set to the eggs while keeping the hash warm. Expect a faint roasted aroma and slightly drier surface compared to stovetop eggs. Check early if you prefer runny yolks, and remember that residual heat continues to cook after you remove the skillet, so aim for slightly less than your ideal finish time.
I prefer a super runny yolk, so I like to cook them separately: Cooking eggs in a separate pan ensures precise control, yielding a lusciously runny yolk when you want it. Frying or poaching separately also lets you manage the texture independently from the hash, which can be especially helpful when serving multiple people with different preferences. The main pitfall is timing, so coordinate the finishing of the eggs with the hash so everything is hot together.