Mix grated carrot, red onion, green chiles, garlic, diced tomatoes, and sea salt together in a mixing bowl. Cover and chill 1 hour before serving.
Combine hash and eggs in a skillet and cook over medium high heat, stirring frequently, until eggs are set and no longer runny, 6 to 8 minutes. Season with pepper to taste.
Spoon filling into cabbage leaves and top with salsa.