Heat the olive oil in a large skillet over medium-high heat.
Add the diced sweet potato to the pan and cook for 8 to 10 minutes, stirring occasionally, until the edges are golden and the centers are tender.
Add the ground turkey to the skillet, using a spatula to break the meat into small crumbles.
Season the mixture with sea salt, black pepper, garlic powder, and onion powder, stirring well to incorporate the spices.
Continue cooking until the turkey is fully browned and no longer pink.
Stir in the chopped kale and add the tablespoon of water to the skillet.
Cover the pan with a lid for 2 minutes to allow the kale to steam and wilt into the hash.
Remove the lid, give everything one final toss, and serve immediately while hot.