Step 1: Prepare your ingredients. Dice your leftover prime rib into 1/2 to 3/4-inch cubes. Peel and dice your potatoes into uniform 1/2-inch cubes. Thinly slice your onions. Mince the garlic and chop any fresh herbs you're using.
Step 2: Heat a large, heavy-bottomed skillet (cast iron works wonderfully here) over medium-high heat. Add 1 tablespoon of olive oil or butter. Once shimmering, add the diced potatoes in a single layer. Cook for 8-10 minutes, flipping occasionally, until golden brown and tender. Season with salt and pepper. Remove the potatoes from the skillet and set aside.
Step 3: Reduce the heat to medium. Add another tablespoon of olive oil or butter to the same skillet. Add the sliced onions. Cook slowly, stirring occasionally, for 10-15 minutes, until they are soft, deeply golden brown, and caramelized.
Step 4: Add the minced garlic and chopped fresh rosemary/thyme (if using) to the caramelized onions. Cook for another 1-2 minutes until fragrant.
Step 5: Add the diced prime rib to the skillet with the onions and garlic. Stir to combine. Cook for only 3-5 minutes, just until the prime rib is warmed through. Remember, the prime rib is already cooked, so you don't want to overdo it and dry it out. If using, add the optional beef broth to deglaze the pan and add moisture.
Step 6: Return the crispy potatoes to the skillet. Gently fold everything together. Taste and adjust seasoning with additional salt and pepper as needed.
Step 7: Optional: For an extra touch of deliciousness, make four wells in the hash and crack an egg into each well. Cover the skillet and cook for 3-5 minutes, or until the egg whites are set and the yolks are still runny.
Step 8: Serve immediately, garnished with fresh parsley or chives, if desired. Enjoy your elevated prime rib experience!