Boil the sweet potato until very tender, about 12 minutes. Drain it and let it cool. Blend the potato and chickpeas in a food processor. Add the other ingredients and blend until smooth, about 1 minute. Place the dip in a bowl and refrigerate. Before serving, add a sprinkle of paprika, if you like.
Heat the oven to 350°. Slice each pita into four equal pieces, then split each in half. Lay all the halves on two baking sheets. In a small bowl, whisk together the next four ingredients. Brush the tops of the pita pieces with the mixture, then sprinkle with the Parmesan. Bake until browned and crispy, about 12 minutes. Serve with the hummus.