Peel the eggplants and dice them into 1-inch cubes. Place the cubes in a large colander and toss them with 1 1/2 teaspoons salt. Let them drain in the colander over a bowl in the sink for 30 minutes to remove excess moisture.
Combine the breadcrumbs with the Parmesan cheese in a large bowl. In a second bowl, whisk together the eggs with 2 tablespoons water. Place the flour in a third bowl. Bread the eggplant cubes in batches by coating them in the flour, then the eggs and then the cheesy breadcrumbs.
Line a baking sheet with paper towels.
Add three inches of oil to a large, heavy-bottomed pot set over medium heat and attach the deep-fry thermometer. Once the oil reaches 360ºF, add the breaded eggplant in batches, cooking them until they're golden brown on all sides. Using a slotting spoon, transfer the eggplant to the paper towel-lined baking sheet and immediately season them with salt. Repeat the frying process with the remaining eggplant, returning the oil to 360ºF between each batch.
Garnish the eggplant bites with chopped fresh parsley and serve them with marinara sauce for dipping.