For the coleslaw:
1) 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.
2) Cover and chill until serving time.
For the pesto:
1) Place all of the ingredients except the tomatoes in a small food processor; process briefly until the mixture forms a coarse paste.
2) Transfer to a small bowl and gently stir in the tomatoes. Cover and set aside.
For the burgers:
1) Prepare a medium-hot fire in a charcoal barbecue with a cover, or preheat a gas griddle to medium-high.
2) Combine the coconut milk, lime zest, and lime juice in a 25cm fire-proof pan. Place the frying pan on the griddle rack and bring the mixture to a simmer. Continue cooking, stirring occasionally, until the mixture is thickened and reduced to 185ml, about 15 minutes. Add the curry paste to the mixture and whisk until smooth. Transfer to a small bowl to cool.
3) 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.
4) When the griddle is ready, brush the 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 griddle to toast lightly.
5) Distribute an equal amount of the coleslaw on the bottom buns. Top each with a patty and a dollop of the pesto.
6) Add the bun tops and serve.