Sprinkle the eggplant slices on both sides with a little coarse salt. Layer them in a non-aluminum colander and let drain for at least 1 hour. Remove the eggplant slices and pat dry. In a food processor or blender, combine the anchovies, capers, parsley, and lemon  juice and process until smooth. Brush each side of the eggplant slices with a bit of olive oil. Grill the eggplant for 3 to 4 minutes per side, or until brown and soft. Spread the anchovy mixture on  half of the eggplant slices, cover with the cheese and top with the remaining eggplant. Grill until the cheese is soft. If the sandwiches are large, cut them into halves or thirds. Serve at once. Makes 8 sandwiches