In the bowl of a food processor, add the olives, sun-dried tomatoes and the olive oil it was packed in. Pulse until smooth, but still chunky. Add more extra-virgin olive oil if mixture is too dry. Spoon into a serving bowl. If not serving immediately, cover tightly with plastic wrap and refrigerate up to 2 days. Be sure to bring it to room temperature and to mix it thoroughly before serving.
Gently pull off the leaves from the endive, being carefully not to tear the leaves. Wash thoroughly with cold water and dry completely.
Place the bowl of tapenade in the center of a large platter. Decoratively circle the tapenade bowl with the endive leaves working your way to the rim of the platter.