In a medium skillet, toast pistachios over medium heat, stirring frequently, until fragrant and golden, about 7 minutes. Transfer to a plate; let cool. In a large bowl, whisk together 1/4 cup oil and vinegar; season with salt and pepper, and set dressing aside.
Heat remaining tablespoon oil in skillet over medium. Sprinkle chicken with coriander; season with salt and pepper. Cook (in batches if necessary), turning once, until opaque throughout, 2 to 3 minutes per side. Transfer to a cutting board, and thinly slice crosswise.
Add pistachios, lettuce, parsley, and scallions to bowl with dressing, and toss to combine. Divide among serving bowls; top with chicken, feta, and oranges.
Cooking nuts in a skillet just until golden makes them extra crunchy and intensifies their flavor. Remove them from the skillet right after toasting to prevent overbrowning.