Add the yogurt, feta, garlic powder, za’atar, lemon juice and pepper to a food processor or blender and whip until smooth. If making ahead, chill before serving.
To make the seasoned naan, preheat the oven to 375F. Line a baking sheet with parchment paper. In a small bowl, stir together olive oil, za’atar and salt.
Stack the naan on top of one another slicing each into 8 triangles, as you would a pizza. You can leave it whole if you prefer. Arrange the naan on the baking sheet and brush all sides with half of the seasoned olive oil, reserving the remaining half for drizzling on top of the whipped feta yogurt. Bake about 6 minutes, until the naan is fragrant and warmed through.
To serve, spoon the whipped feta yogurt into a shallow bowl. Drizzle the remaining seasoned olive oil. Sprinkle with parsley and additional za’atar, if you like. Serve with the warm naan.