How to Make It
Place eggplant slices in a large bowl; sprinkle with salt, tossing to coat both sides. Let stand, uncovered, until moisture forms on eggplant and water collects in bottom of bowl, about 30 minutes.
Rinse eggplant slices well under cold running water. Squeeze each slice between paper towels to remove excess water, and pat dry with paper towels.
Pour oil into a large, high-sided skillet to a depth of 1/2 inch. Heat over medium-high to 340°F. Working in batches, use a spider to drop eggplant slices into oil. Fry until golden, about 3 minutes per side. Remove from oil, and drain on a paper towel–lined baking sheet. Pat tops of eggplant slices with paper towels to remove excess oil.
Stir together walnut paste and 2 tablespoons water in a large bowl, adding more water, 1 teaspoon at a time, if necessary, until mixture is spreadable. Add basil and jalapeño; stir to combine.
Spread about 2 tablespoons walnut mixture on one end of each eggplant slice, and roll up. Arrange rolls, seam side down, on a serving platter. Spread tops with any remaining walnut mixture, and sprinkle evenly with pomegranate arils.