Heat oven to 200C/180C fan/gas 6. Cut the polenta into thick chips and rub all over with a little oil. Spread out over a baking sheet and cook for 20 mins until golden. Cut each chicken breast in half, lightly flatten using a rolling pin or heavy can, then rub all over with oil. Spread the breadcrumbs and Parmesan out on a plate, then dip in the chicken to coat.
Place the chicken on another baking sheet and cook for 10-12 mins until just crisp and cooked through. Place a mozzarella slice on top and return to the oven until starting to melt. Pile the burgers onto buns with some salad leaves, tomatoes and a dollop of pesto. Serve with the polenta chips.