Prep the potatoes. In a medium saucepan, add diced potatoes and cover with water. Bring water to a boil and cook potatoes until they are slightly soft, but not mushy, about 10-12 minutes. Drain sweet potatoes and set aside. if prepping potatoes in advance cool for future use.
Place a large sauté pan on medium heat add half tbsp of oil, add sausage and potatoes. Allow cooking on one side until the edges of the sausage/potatoes begin to brown, about 3 minutes. Using a spatula, gently flip the sausage and potatoes to one side of the pan.
Add remaining oil to the pan, and turn heat to medium-high. Add onion, bell pepper, celery and broccoli to the free side of the pan. Sauté until vegetables begin to brown, moving to prevent burning, about 3 minutes. Gently fold the sausage, potatoes, and vegetables together and season with paprika, garlic powder, salt and pepper. Allow hash to cook for another 1-2 minutes, to allow flavors to meld. Meanwhile cook eggs to preference.
Adjust seasoning of hash and transfer to serving platter or bowls. Top with eggs, and garnish with scallions and parmesan cheese. Serve immediately.