These quesadillas are great as a starter, but also perfect for a simple lunch or a light summertime dinner.
1. Cut the peaches in half and remove the pits.
2. Place the peaches, cut sides down, on a hot grill. Cook for 3-5 minutes, until they begin to soften and show grill marks.
3. Let the peaches cool slightly so they’re easier to handle, then slice thinly.
4. Brush one side of each tortilla lightly with oil. Place the tortillas, oil sides down, on the hot grill.
5. Evenly divide the shredded cheese between the tortillas.
6. Layer sliced peaches over one half of each tortilla only, leaving the other half covered with just cheese.
7. Sprinkle the basil and chives evenly over the peaches.
8. Allow the quesadillas to cook until the cheese is almost fully melted. Carefully fold the cheese-only half of each tortilla over the peach and herb filling, pressing down gently to help the quesadillas stick together.
9. Let the quesadillas cook for one minute more, just until the cheese is completely melted. Remove from the heat, slice each quesadilla in half, and serve.