In a large skillet, heat the oil over medium-high heat. Add the shallot, leek, mushrooms, salt, and pepper. Cook, stirring frequently, until the vegetables are soft, about 8 minutes. Add the kale and cook until wilted, about 8 minutes. Add the broth and cranberries. Bring to a boil and scrape up the brown bits that cling to the bottom of the pan with a wooden spoon.
Remove the pan from the heat and stir in the goat cheese. Divide the filling among the wraps. Fold the bottom of each wrap up and roll in the sides, like a burrito, and cut in half. Serve hot.