Heat the oven to 400°F. Cook ziti in water with the tablespoon salt until 2 minutes short of the package time, then drain.
Season chicken with 1/4 teaspoon salt and pepper. Coat lightly in flour, dip in beaten egg and press into panko mixed with Parmesan; discard leftover coating ingredients that touched raw chicken.
Heat 2 tablespoons oil in a large skillet over medium heat. Cook chicken in two batches for 3 to 4 minutes per side until golden and at least 165°F, adding remaining oil for the second batch; transfer to a clean plate.
Lower heat and stir garlic in the skillet for 30 seconds. Add tomatoes, basil and remaining salt and simmer for 5 minutes, then fold in ziti and transfer to a 9-by-13-inch baking dish.
Arrange breaded chicken over the pasta and scatter mozzarella over it. Bake uncovered for 12 to 15 minutes until the cheese melts and the center is hot at 165°F.
Rest for 5 minutes and spoon from underneath to serve some sauced pasta and crisp-topped chicken together.