For the pie crust, add the flour, butter, eggs, salt, and baking powder to a bowl and knead until a smooth dough forms. Wrap the dough in plastic wrap and refrigerate for 1 hour.
For the pulled chicken, heat some olive oil in a pan over medium heat. Season the chicken breasts with salt and pepper and sear the meat on both sides until golden brown. Add a little bit of water to the pan, cover with a lid, and let the chicken cook for about 10 minutes. Use 2 forks to shred the meat and set the pulled chicken aside.
For the filling, heat the olive oil in a pot over medium heat and sweat the onion and garlic. Stir in the pulled chicken, paprika, tomato paste, salt, pepper, and chicken broth. Bring the mixture to a boil and add the green olives and corn. Combine the corn starch and milk and pour the mixture into the pot. Stir everything until combined and let thicken.
Take a fist-sized portion of the pie crust dough and set it aside for the top crust. Line the bottom and sides of a springform pan with the rest of the dough and spoon the filling over the bottom crust. Spread cream cheese over the filling and sprinkle shredded mozzarella cheese on top.
Roll out the piece of dough that you set aside earlier and place it on top of the pie. Brush the egg wash over the top crust and make a diamond pattern in the dough with a knife. Transfer the springform pan to a preheated oven and cook at 325°F for 50 minutes.