Layered Eggplant, Zucchini and Tomato Casserole

extra-virgin olive oil, plus more for greasing and brushing

medium zucchini (1 1/2 pounds), sliced lengthwise 1/4 inch thick

long, narrow eggplants (1 1/2 pounds), peeled and sliced lengthwise 1/3 inch thick

Salt and freshly ground pepper

large shallot, minced

plum tomatoes, cut into 1/2-inch dice

feta cheese, crumbled (3/4 cup)

chopped basil

panko or coarse dry bread crumbs