Step 1In a bowl, combine the red pepper flakes, half of the garlic and one-half cup of olive oil. Let stand until ready to grill the eggplant.
Step 2Using a large mortar and pestle, crush the remaining garlic, the walnuts and one-fourth teaspoon salt to a paste. Add the paprika, then slowly add three-fourths cup olive oil, stirring it in with the pestle. The sauce should have the consistency of a loose, coarsely ground peanut butter.
Step 3Stir in the cilantro, grinding it with the pestle to release its oils. Stir in the lemon juice. Taste and adjust the seasoning. Be particularly careful with the salt; the sauce should not be overtly salty, but I usually have to add a little more (about one-fourth teaspoon) to get the full flavor of the walnuts. Makes 1 cup sauce. Set aside until ready to use.
Step 4Slice the eggplants about one-half inch thick, leaving the slices attached at the stem end. Brush the cut surfaces with the flavored olive oil and grill over medium heat. Turn the eggplant frequently so it cooks through without scorching. Before each turn, brush lightly with the olive oil. You'll know the eggplant is cooked through when it flops lazily when you turn it, about 8 to 12 minutes.
Step 5Arrange the eggplants on a platter, spreading the cut slices slightly. Spoon over half of the walnut sauce and pass the remainder at the table.