Peel the sweet potato and cut it into small 1/2-inch cubes to ensure even cooking and a consistent texture.
Heat the extra virgin olive oil in a large cast-iron skillet over medium-high heat until shimmering.
Add the diced sweet potatoes to the skillet and sauté for 5 minutes, stirring occasionally to brown the edges.
Pour the water into the skillet and immediately cover with a tight-fitting lid for 3-4 minutes to steam the potatoes until just tender.
Remove the lid, push the potatoes to the outer edges of the pan, and add the ground pork to the center.
Break up the pork with a spatula and season the entire skillet with sea salt, black pepper, garlic powder, onion powder, and smoked paprika.
Cook the pork undisturbed for 3 minutes to develop a crust, then stir and continue cooking until fully browned.
Stir in the shredded green cabbage and sauté for another 3-4 minutes until the cabbage is wilted and the potatoes are golden and crisp.
Adjust seasoning if needed and serve immediately while the skillet is piping hot.