Preheat oven to 350 degrees F.
Cut phyllo into six-inch squares. Place one sheet into each of the four-inch baking dishes. Brush each with butter. Repeat, layering phyllo at different angles to create texture, until all sheets are buttered.
Crack one egg into each of the four dishes. Top each with equal portions kale and cheese.
Bake for approximately 20 minutes each or until cheese and phyllo are browned. Serve warm.