Preheat oven to 400°F/200°C.
Remove the sausage meat from the casings and add to a mixing bowl. Add the Parmesan cheese, egg and basil. Mix well using a fork until combined, set aside.
Trim the top and bottom off the eggplants. Stand the eggplant on its end and trim a thin slice off the skin. Cut 5 slices, ¼-inch (1/2 cm) thick from each eggplant to yield a total of 12 slices. Lay the slices onto a board and sprinkle lightly with salt. Let sit for 20 minutes to draw out the moisture.
Preheat a heavy or cast iron skillet over medium heat. Dry the eggplant slices and place in the pan (no need for oil). Cook for 2-3 minutes per side, just until they start to soften. Remove and allow to cool.
Add a thin layer of marinara sauce to the bottom of an 8 x 8-inch (20 x 20cm) casserole dish.
Divide the sausage into 12. Place the sausage 1/3 of the way into the center an eggplant slice. Roll the eggplant over the meat and place, seam-side down into the dish. Repeat with all of the eggplant slices and sausage, arranged an even layer.
Pour the rest of the marinara sauce on and around the eggplant. Top with mozzarella, cover tightly with foil and bake for 10 minutes. Remove the foil and bake for 20 more minutes until the temperature of the sausage is 165°F/73°C when a meat thermometer is inserted.
Serve warm topped with grated Parmesan and basil.