Adjust oven rack to lower-middle position and heat oven to 375 degrees. Melt butter in 10-inch nonstick skillet over medium heat. Add spinach, salt, and pepper and cook until mixture is dry, about 4 minutes. Stir in garlic, nutmeg, and cayenne and cook until fragrant, about 30 seconds. Transfer mixture to large bowl and let cool slightly, about 5 minutes.
Stir feta, ricotta, scallions, eggs, mint, and dill into cooled spinach mixture until well combined. Spread mixture evenly into now-empty skillet.
Working with 1 sheet phyllo at a time, lay flat on clean counter and spray liberally with oil spray. Crumple oiled phyllo into 2-inch ball and place on top of spinach mixture in skillet.
Transfer skillet to oven and bake until phyllo is golden brown and crisp, about 25 minutes, rotating skillet halfway through baking. Remove skillet from oven (skillet handle will be hot). Let cool for 10 minutes before serving.