Scrub the potato and dice into 1/2-inch cubes; finely chop the onion and halve the cherry tomatoes.
Heat the olive oil in a large non-stick or cast-iron skillet over medium-high heat.
Add the ground turkey to the skillet, breaking it up with a spatula, and cook until browned and cooked through.
Stir in the diced potatoes and onions, seasoning with sea salt, black pepper, garlic powder, and smoked paprika.
Reduce heat to medium, cover the pan, and cook for 8-10 minutes, stirring occasionally, until the potatoes are tender and golden-brown.
Toss in the cherry tomatoes and cook for 1-2 minutes until they begin to soften and blister.
Use a spoon to create three small wells in the hash and crack one egg into each opening.
Cover the skillet again and cook for 3-4 minutes, or until the egg whites are set but the yolks remain runny.