Place lemon juice, tahini, garlic, and salt in the bowl of a food processor; process until smooth. Add garbanzo beans and 1/2 cup olive oil; process until smooth, scraping sides of the bowl occasionally. Add sun-dried tomatoes; pulse until chopped to very small pieces and incorporated into hummus. Add basil; pulse until mixed in, about 3 pulses.

Transfer hummus to a shallow serving dish; make a few decorative grooves on top. Refrigerate at least 1 hour. Drizzle with 2 tablespoons olive oil; sprinkle with paprika before serving.