Place a cooling rack over a baking sheet. Lay the eggplant slices on the rack, generously salting each slice (about 1/4 teaspoon per slice). Place another baking sheet on top of the eggplant and weigh it down with a few cans. Let them sit 30 minutes. Flip the eggplant slices, sprinkle with more salt, weigh down again and let them sit for another 30 minutes. (This draws out the bitter juices.) Meanwhile, toast the walnuts.
Preheat the oven to 350 degrees F. Spread the walnuts on a small baking sheet and pop into the oven until the walnuts give off their nutty aroma and deepen in color, about 5 minutes. When they are cool enough to touch, chop them finely.
Make the ricotta filling: Push the ricotta through a sieve into a medium bowl. This gives the cheese a light, airy texture. Add the toasted walnuts, garlic, mint, date, half the lemon juice, a pinch of salt and a swirl of olive oil. Stir together, taste for seasoning and then set aside.
Rinse the eggplant slices well and pat them dry. Warm a grill pan over moderately-high heat. Brush the eggplant slices with olive oil on one side; place the oiled-side down on the hot griddle and brush the other side. Cook until browned, about 2 minutes, then flip and cook another 2 minutes.
To assemble the rolls, place a couple of tablespoons of filling at one of end of a slice of eggplant. Roll and place on a plate seam-side down. Top the eggplant rolls with the remaining lemon juice, a swirl of extra-virgin olive oil and the reserved mint leaves, torn over the dish. Serve hot or at warm temperature.