Stem the Fresno chile and slice into thin rings. Stir into the honey and let rest for 1 hour at room temperature. Remove the chile slices using tweezers, chopsticks or a mesh colander. Discard slices and reserve the honey.
Prepare the grill for direct grilling over high heat.
Slice each peach into 8 wedges, discarding the pit. Grill both sides of the peach slices over a hot fire until brown grill marks are evident. Remove from the grill before the peaches become too soft about 3-4 minutes.
To serve, place the peaches and burrata on a salt block. (If you don’t have a salt block, use a plate and lightly sprinkle the dish with sea salt to add that umami flavor.) Break into the burrata to open up the creamy center. Drizzle with chile-infused honey and top with Thai basil leaves.
Serve immediately, while the peaches are still warm and before the saltiness from the salt block turns from subtle to overwhelming.
