01 - In a small bowl, combine softened butter, chopped pickles, dill, Dijon mustard, lemon zest, salt, and pepper. Mix well, then refrigerate until needed.
02 - Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the sausage, breaking it up with a spatula, and cook until browned and cooked through, about 5 minutes. Remove sausage from skillet and set aside.
03 - Add remaining olive oil to the same skillet. Add potatoes and cook, turning occasionally, until golden and starting to crisp, about 10 minutes.
04 - Add onion, red and green bell pepper, and garlic to the potatoes. Season with salt, pepper, and smoked paprika. Sauté until vegetables are tender and potatoes are cooked through, about 8-10 more minutes.
05 - Return the sausage to the skillet and stir to combine. Taste and adjust seasoning if necessary.
06 - Make four wells in the hash. Crack one egg into each well. Reduce heat to low, cover the skillet, and cook until eggs are set to your liking, 5-7 minutes.
07 - Remove skillet from heat. Dot the hash and eggs generously with the pickle butter. Sprinkle with chopped parsley and serve immediately.