Prepare all of the ingredients. Preheat oven to 425deg.
In a small bowl, combine ingredients for dressing and place in refrigerator.
In a sauce pan, add all ingredients for chicken. Bring to boil and let cook for 15 minutes. Once done, remove chicken from broth and shred. Set aside to cool before adding to salad.
Brush each side of the bun with avocado oil and place on baking sheet. Put in oven for 10-12 minutes until toasted golden brown.
In a large bowl, combine remaining ingredients. Add cooled shredded chicken. Fold in dressing.
To serve, spoon a serving of chicken salad. You could garnish with additional dill or feta. You could also add some chopped Kalamata Olives if desired.