Cook the hash browns: Add the oil and butter to a heavy-bottomed skillet over medium heat. Saute the potato, salt, and paprika until the potatoes are golden brown and tender. Turn down the heat if needed. Season with salt and pepper to taste.
For the sausage: Cook in a pan over medium heat on both sides until nicely browned to an internal temperature of 160°F (71°C) using a thermometer.
Heat a nonstick pan on medium heat; melt the butter in the pan and crack the eggs in, being careful not to break the yolks. Cook until the whites of the eggs firm up and set. Season with salt and pepper.
Serve the eggs with sausage, hash browns, mango, and orange juice.