In a mixing bowl, combine flour, baking powder, and salt. Add water and olive oil to the mixture and stir until dough forms.
Knead the prepared dough on a floured surface for about 5 minutes, so it becomes smooth. Cover it with a wet cloth and let it rest for 15 to 20 minutes.
In a large bowl, mix together shredded chicken, mozzarella cheese, ranch or Caesar dressing, and green onions. Add salt and pepper to taste.
Preheat oven to 400ºF (200ºC), and divide dough into equal parts.
Roll each piece into a rectangle on a floured surface, putting a nice amount of chicken filling in the center of each rectangle.
Fold the sides over the filling and roll it up tightly, sealing in the edges.
Place chicken bakes seam-side down on a baking sheet lined with parchment paper.
Brush the tops with olive oil and, if desired, sprinkle with more mozzarella cheese.
Bake in the preheated oven for about 20-25 minutes, or until golden brown and cooked through.
Let the chicken bakes cool a bit before slicing them. Serve warm and enjoy your homemade chicken bakes!