Preheat oven to 375 degrees F. Thoroughly coat a baking sheet with oil. Set aside. (You may need to use two sheets.)
In a shallow bowl, whisk together the eggs and 1 tablespoons water. In another bowl (a pie plate works well), combine the panko or Rice Chex crumbs, Parmesan, Italian seasoning, salt and pepper.
Cut the eggplants into thick rounds. (I like them to be between 1/2 and 3/4 inches thick so they have time to brown in the oven before they become too soft.) Dip the eggplant slices in the egg mixture, letting the excess drip off. Dredge the dipped slices in the Parmesan mixture, pushing down gently to coat well. Transfer the coated slices to the baking sheet.
Bake until golden brown on the bottom, 17-20 minutes. (Peek underneath using a spatula; if they aren’t yet golden, give them a few more minutes and check again.) Flip the slices and continue baking until lightly browned on other side but still slightly firm, about 10 minutes more. All ovens vary, so don’t hesitate to adjust a few minutes either way. You want the first side to be golden brown; then worry more about doneness and texture than getting the second side equally browned. (When pressed for time, I have simply given the tops a quick broil rather than flipping and cooking for the additional 10 minutes.)
Remove from the oven, and serve as is or with a side of marinara sauce for dipping.