Place the chickpeas, tahini, sun-dried tomatoes, lemon juice, garlic, and salt in a food processor.
Process until smooth, scraping down the sides and adding 2-3 tablespoons of water until the hummus reaches a creamy and spreadable consistency. Taste and adjust for salt if desired.
Spread ¼ of the hummus on each tortilla, all the way to the edges.
Evenly distribute ¼ of the spinach leaves on top of the hummus on each tortilla, leaving a ½-inch border around the edges, followed by ¼ of the tomatoes, olives, and basil.
Tightly roll up the tortillas, finishing with the seam side down. Cover and chill in the refrigerator for 30 minutes to make them easier to slice.
Lightly slice the rolled-up tortillas into ¾-inch pieces with a serrated knife.
Arrange the pinwheels on their sides before serving.