Wash the russet potato and dice it into small, uniform 1/2-inch cubes to ensure even cooking.
Heat the olive oil in a large non-stick skillet over medium-high heat.
Add the diced potatoes to the skillet in a single layer and cook for 8 to 10 minutes, stirring occasionally, until they are golden brown and fork-tender.
Push the potatoes to one side of the skillet and add the ground turkey to the empty side, breaking it apart with a wooden spoon.
Add the diced red bell pepper and yellow onion to the turkey and season the entire pan with sea salt, black pepper, garlic powder, and smoked paprika.
Sauté the mixture for another 5 to 7 minutes until the turkey is fully browned and the vegetables have softened.
Create a small well in the center of the hash and crack the egg into it.
Cover the skillet with a lid for 2 to 3 minutes, or until the egg white is set but the yolk remains runny.
Slide the hash onto a plate and serve immediately while the potatoes are still crispy.