Blanche green beans in lightly salted boiling water 2-3 minutes until beans are fork-tender. Immediately plunge beans in ice water to cool them. Drain beans and place in a large bowl. Set aside.
Place basil, lime juice, avocado, agave, and garlic in a food processor. While processing, drizzle olive oil through top until dressing is smooth, scraping down sides if necessary. Season dressing with salt and pepper to taste.
Pour dressing over cooled green beans and stir in feta and cherry tomatoes. Toss green beans until evenly coated with dressing. Chill salad until ready to serve. Enjoy!