Cook the pasta according to package instructions until al dente.
Drain and rinse the cooked pasta under cold water.
In a large bowl, whisk together olive oil, lemon juice, lemon zest, salt, and pepper to create the dressing.
Add the cooked pasta to the bowl, tossing it in the dressing until fully coated.
Fold in the tarragon, cherry tomatoes, cucumber, and feta (if using).
Taste and adjust seasoning, if needed.
Let the pasta salad sit in the refrigerator for at least 30 minutes before serving.
Serve chilled or at room temperature, garnished with additional tarragon if desired.