Slice each chicken breast in half horizontally so you have 4 pieces. Season the chicken on both sides with salt and pepper. Set aside.
In a pot, heat the tablespoon of oil cook the onion until soft, then add the potatoes and carrot, cook for about 1 minute then add the water and bring to a boil then reduce to a simmer and let cook for about 10 minutes.
Add the curry paste to the pot and stir to dissolve and cook for another 10 minutes on a low simmer then remove from heat.
To cook the chicken, you can use a deep fryer or a heavy skillet with about 1/2 inch of oil, heated to about 180 C, hot but not smoking. Set out 3 shallow dishes, first one for the flour, second one for the beaten eggs, third one for the panko.
While the oil is heating, 1. coat the chicken with flour and shake off the excess. 2. dip the chicken into the beaten egg. 3. roll the chicken in the panko. 4. dip in the egg again. 5. roll in the panko again, 6. set aside. When the oil is hot, fry until golden brown and remove and set on paper towels to drain. Optional, top each piece of chicken as soon as you take it from the hot oil with a slice of cheese.
To assemble this dish, the common way is to put rice on one side of each dish, then take a piece of chicken and slice into 1/2 slices, then pick all of that up with a spatula and place this on top of the rice at a bit of an angle, lower towards the empty side of the dish, then take a scoop or two of curry and pour over half of the chicken then the rest in the open part of the dish. Serve.