Arrange the eggplant slices in a single layer on a clean surface.
Sprinkle the slices with coarse salt, and set aside for 10 minutes. Remove the excess moisture and salt with a paper towel.
In a greasy grill pan, place the eggplant slices, and grill for about 3 minutes per side. The pictures above illustrate these 2 steps. (Please, don't skip the steps 3 and 4. They are very important to avoid the lasagna becoming too soupy.)
In a medium bowl, mix the ricotta cheese, Parmesan cheese, and an egg. Stir well.