Peel and dice the sweet potato into small, even cubes. Dice the onion and bell pepper as well.
In a medium skillet, heat 1 teaspoon of olive oil over medium heat. Add the diced sweet potato, and sauté for about 5 minutes.
Add the diced onion and bell pepper, and continue cooking until the sweet potato is tender and the vegetables are slightly caramelized, about another 5-7 minutes. Season with salt and pepper.
In a separate pan, warm the turkey sausage over medium heat until heated through and lightly browned. If using pre-cooked sausage, simply slice it into rounds and add it to the hash towards the end of cooking.
Combine the sausage with the vegetable hash and set aside.
Fill a medium saucepan with water and bring it to a simmer. Gently crack the eggs into small cups, then slide them into the simmering water. Poach the eggs for about 3-4 minutes for a runny yolk or longer if desired.
While the eggs are poaching, prepare the avocado sauce by mashing the 1/4 avocado in a small bowl, mixing in 1 tablespoon of lime juice, and seasoning with a pinch of salt until smooth.
Plate the crispy sweet potato hash with sausage, and top with the poached eggs. Drizzle the creamy avocado sauce over the top or serve on the side.
Finish with an extra sprinkle of salt and pepper if desired and serve immediately.