How to Make It
Using a vegetable peeler, cut eggplants lengthwise into strips. (Do not use centers of eggplants with seeds.) Arrange eggplant strips on a baking sheet lined with paper towels. Top with a layer of paper towels and a second baking sheet. Let stand 10 minutes. Divide eggplant strips evenly into 4 piles.
Combine parsley, garlic, zest, juice, and 1/2 cup each of the walnuts and Parmesan in a blender. Process on low speed until mixture is roughly chopped, stopping to scrape down sides as necessary. With blender running, slowly drizzle in 1 cup of the oil through food chute, and process until mixture is well blended and no chunks remain, about 1 minute. Stir in pepper and 1/2 teaspoon of the salt.
Heat 1 tablespoon of the oil in a large nonstick skillet over high. When oil is shimmering and nearly smoking, add 1 pile of eggplant strips; cook, without stirring, until lightly browned on bottom, 30 seconds to 1 minute. Stir with tongs to redistribute, and cook, without stirring, 30 seconds. Remove from heat, and stir in 1/4 cup of the parsley pesto. Transfer to a bowl, and wipe skillet clean. Repeat procedure 3 times with remaining 3 tablespoons oil, 3 piles of eggplant strips, 3/4 cup of the parsley pesto, and 3 bowls.
Sprinkle each serving with 1 tablespoon each of the Parmesan and walnuts. Serve with additional parsley pesto.