Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high.
For the slaw: Whisk together the lime juice and sugar in a medium-sized bowl to dissolve the sugar. Add the pear and carrot and toss to coat. Cover and chill until serving time.
For the pesto: Place all of the ingredients except the tomatoes in a small food processor; process briefly until the mixture forms a coarse paste. Transfer to a small bowl and gently stir in the tomatoes. Cover and set aside.
For the patties: Combine the coconut milk, lime zest, and lime juice in a 10-inch fire-proof skillet. Place the skillet on the grill rack and bring the mixture to a simmer. Continue cooking, stirring occasionally, until the mixture is thickened and reduced to 2/3 cup, about 15 minutes. Add the curry paste to the mixture and whisk until smooth. Transfer to a small bowl to cool.
Place the chicken in a large mixing bowl. Add the cooled coconut milk mixture, basil, panko and salt. Using a large fork, mix the ingredients together gently but thoroughly. Divide the mixture into 6 equal portions and form the portions into patties to fit the buns, making a slight indentation in the center of each patty.
When the grill is ready, brush the grill rack with oil. Place the patties on the rack, cover, and cook for 4 minutes. Flip the patties, cover, and cook an additional 4 minutes, or until the juices run clear from the center of the patties when pierced. During the last few minutes of cooking, arrange the buns, cut side down, around the edges of the grill to toast lightly.
To assemble the burgers: Distribute an equal amount of the slaw on the bottom buns. Top each with a patty and a dollop of the pesto. Add the bun tops and serve.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.