Dak Dori Tang Spicy Korean Chicken Stew

Name: Dak Dori Tang (Spicy Korean Chicken Stew)
Ingredients: 0.25 cup soy sauce; 3 tablespoons gochujang (Korean hot pepper paste); 1 tablespoon brown sugar; 1 tablespoon minced garlic; 2 teaspoons sesame oil; 1.5 teaspoons minced fresh ginger root; 0.5 teaspoon chile powder; 2 tablespoons vegetable oil, divided, or as needed; 2 skinless, boneless chicken breasts, cut into 1-inch cubes; 3 carrots, peeled and thickly sliced; 2 potatoes, peeled and diced; 1 leek, trimmed and thinly sliced; 1 small onion, cut into 8 wedges; 1 habanero pepper, seeded and minced; 2 cups water, or as needed