Add flour, baking powder, and salt to a mixing bowl. Blend with a fork. Add yogurt, olive oil and the water, and mix just until everything is well-incorporated and you can form the mixture into a ball. Don’t over mix.
Place dough on a floured board and if it is still a bit sticky, just knead a few seconds with enough flour to make it smooth. Divide dough into 12 pieces and form each into a ball shape. Allow the dough balls to rest, covered, for at least 15 minutes. You can let it rest longer, too. When we’ve made this recipe, we’ve let the dough rest, covered, for up to an hour at room temperature before cooking it.
Before you cook the bread, whip the feta by putting it in your mixer bowl along with the olive oil and beat with the whisk attachment until creamy and as smooth as possible. Then add the yogurt and whip until light and fluffy. If you don’t have a standing mixer, just use a hand-held beater or food processor. Chop the Kalamata olives, tomatoes and basil and set aside in a separate bowl. (You can do all of this ahead of time and refrigerate it until you’re ready to serve.)
When you’re ready to cook the bread, preheat the cast iron skillet over medium heat. Once the whole surface of the skillet is hot, roll out the dough balls into circles about 6-inches in diameter and about ¼-inch thick.
Put a little bit of olive oil or cooking spray in the pan and place the dough round in the skillet and cook for about 2 minutes, or until you see the bottom beginning to turn golden brown and small air bubbles form. Flip and cook the other side for the same amount of time, or until it looks perfect!
Note* If you make these all at once and want to keep them warm, you can preheat a second cast iron skillet and transfer the cooked ones to that to keep warm, or keep them wrapped in foil in a warm oven until ready to serve. To store, wrap cooled naan in waxed paper and store in a baggie or airtight container in the refrigerator until ready to serve.