Preheat oven to 275 degrees. In a mini food processor, process the basil, olive oil, olives and rosemary to a paste.
Arrange the tomato slices on a large, rimmed baking sheet and season with salt and pepper. Spread about 1 teaspoon of the tapenade over each tomato slice. Bake for 1 1/2 hours until the tomatoes are very tender.