Prick sweet potato all over with a fork, then wrap in a damp paper towel and microwave on high for 6 minutes or until soft. Cool slightly, then remove skin and mash flesh with a fork. Set aside.
Fill a large skillet with 1 inch of water and bring to a simmer. Add kale and cook, stirring, until soft and wilted, about 3 minutes. Drain excess water and shake kale dry.
Wipe out skillet and return to medium-low heat. Place tortilla in skillet, then top half of tortilla evenly with mashed sweet potato, cooked kale, Parmesan, and basil. Fold tortilla over fillings. Cook until cheese is almost melted and underside is lightly browned, 3 minutes. Flip and cook until cheese is completely melted and both sides are lightly browned, about 3 minutes more.
Cool slightly before cutting into 4 pieces.
