Peel the russet potatoes and dice them into uniform 1/2-inch cubes. Rinse them under cold water and pat them thoroughly dry with paper towels; this is crucial for crispy potatoes. Dice the yellow onion and red bell pepper into similar 1/2-inch pieces. Mince the garlic cloves.

Heat a large (12-inch) cast-iron skillet or heavy-bottomed pan over medium-high heat. Add the breakfast sausage (if using ground, break it up; if using links, remove casings and crumble). Cook, stirring occasionally, until browned and cooked through, about 5-7 minutes. Using a slotted spoon, transfer the cooked sausage to a plate lined with paper towels, leaving about 1 tablespoon of rendered fat in the skillet. If there's excess fat, drain it off. If there isn't enough, add 1/2 tablespoon of olive oil.

Add the diced, dried potatoes to the skillet in a single layer. Cook without stirring for 5-7 minutes to allow them to brown and crisp on one side. Stir the potatoes and continue cooking, stirring every 3-4 minutes, until they are tender on the inside and crispy and golden brown on the outside, about 15-20 minutes total.

Push the potatoes to one side of the skillet. Add the diced onion and bell pepper to the empty side. Cook, stirring occasionally, until the vegetables begin to soften, about 5-7 minutes. Add the minced garlic and smoked paprika to the vegetables. Cook for another minute until fragrant.

Return the cooked sausage to the skillet with the potatoes and sautéed vegetables. Stir everything together to combine. Season generously with salt and black pepper to taste. Continue cooking for another 2-3 minutes to allow all the flavors to meld and heat through.

(Optional) For individual servings, you can create four wells in the hash and crack an egg into each. Cover the skillet and cook until the whites are set and yolks are to your desired runniness (about 3-5 minutes). Garnish with fresh chopped parsley, if desired, and serve immediately.