Add salt to a large pot and bring it to a boil over high heat. Add green beans to boiling water and cook for approximately 3-4 minutes (until crisp-tender). Drain the pot and immediately transfer the green beans to a large bowl of ice water.
After beans have cooled, remove them from the ice water and pat them dry. Add them to a large glass bowl or other non-reactive bowl. To the green beans, add tomatoes, basil, parsley, olive oil, and vinegar. Toss to combine. Season with salt and pepper to taste.
Fold in Feta cheese gently. Serve immediately for a warm salad, or chill it in the fridge for a cold salad.