Cook the pasta: Bring a large pot of salted water to a boil.
Cook pasta until just al dente, following package times. Drain and rinse briefly under cool water to stop cooking and prevent sticking. Shake off excess water.
Make the dressing: In a jar or bowl, whisk 1/3 cup olive oil, 2 tablespoons lemon juice, 1 teaspoon lemon zest, 1 tablespoon red wine vinegar, 1 teaspoon Dijon, 1 small clove garlic (grated), 1 teaspoon dried oregano, 1/2 teaspoon honey, 3/4 teaspoon kosher salt, and several grinds of black pepper.
Taste and adjust acid, salt, and sweetness.
Prep the produce: Halve tomatoes, dice cucumber, thinly slice red onion, and halve olives. Chop parsley and/or dill. If using greens, keep them dry and loosely chopped.
Season the chicken: Dice or shred cooked chicken.
Toss with a spoonful of the dressing and a pinch of salt and pepper so it’s flavorful before it meets the salad.
Toss the base: In a large bowl, combine cooled pasta, tomatoes, cucumber, red onion, and olives. Pour in half the dressing and toss to coat.
Add chicken and feta: Fold in the chicken and most of the feta. Add more dressing as needed so everything is lightly glossy but not wet.
Herbs and greens: Sprinkle in chopped parsley and/or dill.
If using spinach or arugula, fold it in gently right before serving to keep it crisp.
Rest and taste: Let the salad sit for 10 minutes so the flavors meld. Taste and adjust with more lemon, salt, or pepper. Finish with the remaining feta on top for a fresh look.
Serve: Enjoy slightly chilled or at room temperature.
A final drizzle of olive oil and a crack of pepper right before serving adds a nice finish.