Combine the breadcrumbs and parmesan in a large shallow bowl or plate.
Coat each chicken piece in pesto. Then place 2–3 basil leaves on each chicken breast and wrap two pieces of prosciutto around each one. Coat the chicken in the panko and parmesan mixture, then transfer to a clean plate.
In a frying pan over high heat, add a generous amount of olive oil. Add the crumbed chicken pieces so they sizzle, then turn the heat down to medium and cook for about 4 minutes on each side (depending on the thickness). Remove and drain on paper towel.
For the burst tomatoes: Place a medium frying pan over medium–low heat. Add the olive oil and 3 cups of the cherry tomatoes and sauté for a couple of minutes. Add the shallots, garlic, thyme and dried herbs and cook gently for 5–7 minutes. Add the honey and red wine vinegar and stir through. Turn off the heat and season really well.
Cut the remaining cherry tomatoes in half and add them to the tomato mixture in the pan. Stir through.
Slice the chicken into pieces and arrange on a platter. Tear off pieces of burrata and scatter them in between the chicken pieces. Drizzle over the burst tomatoes and top with extra basil leaves and pesto. Serve immediately.