Brush Eggplant slices with oil and grill on a barbecue grill or a cast iron grill pan brushed with oil as well.
Grill a few minutes on each side until slices are soft. Transfer to a plate lined with paper towels and sprinkle with salt.
Add the Ricotta, Basil and salt to taste to a blender or a food processor and process till smooth.
To assemble the stacks spoon some tomato sauce into a plate. Using the back of the spoon spread in a circular motion. Layer eggplant, and ricotta using 3 slices per stack. Top with ricotta and spoon some more sauce on top.
Garnish with some fresh basil and grated Parmigiano cheese. Best served at room temperature.