Dough: In a large bowl, combine the flour and butter. Using your hands or a pastry cutter, mix until the mixture resembles coarse crumbs.
Add the water and mix just until the dough comes together. Do not overwork the dough.
Shape into a ball, wrap in plastic wrap, and refrigerate for 20–30 minutes while preparing the filling.
Filling: Place the chicken breast in a pot with 1 liter of water. Bring to a boil, reduce the heat, and cook until an instant-read thermometer inserted into the thickest part of the chicken reaches 165 degrees F, 30 to 35 minutes.
Remove the chicken, shred it, and reserve 330 ml of the cooking liquid.
Heat the oil in a large skillet over medium heat. Add the onion and cook until soft, about 5 minutes.
Add the garlic and cook until fragrant, about 1 minute.
Stir in the shredded chicken, chicken bouillon or salt, paprika, oregano, chimichurri, and black pepper. Mix well.
Add the olives and corn and cook for a few minutes, stirring to combine.
In a small bowl, whisk the flour with 110 ml of the reserved chicken cooking liquid until smooth.
Pour the mixture into the skillet and cook, stirring constantly, for about 3 minutes to cook out the raw flour taste. Add the remaining 220 ml cooking liquid, 226 g softened cream cheese, green onions, and parsley.
Stir well and cook for about 5 minutes, until the filling thickens, becomes creamy, and is well structured. Transfer the filling to a bowl and let it cool before assembling.
Assembly: Preheat the oven to 350°F (180°C). Place the rack in the lower third of the oven.
Remove the dough from the refrigerator and let it sit at room temperature for about 10 minutes to make it easier to work with.
Place a sheet of plastic wrap on the counter and roll out about half of the dough with a rolling pin to the size of the baking dish. Cover with plastic wrap to prevent drying.
Transfer the remaining dough to a 12 × 8-inch (30 × 20 cm) baking dish and press it into the bottom and sides to form the base. Patch any gaps with small pieces of dough if needed.
Brush the edges of the dough with egg white to help seal the top crust later.
Spread the cooled chicken filling evenly over the dough.
Dot evenly with the remaining 300 g of cream cheese over the filling.
Remove the plastic wrap from the rolled dough, place the dough over the filling, then remove the remaining plastic wrap. Press the edges to seal and trim the excess dough.
In a small bowl, whisk the egg with a pinch of sugar and a pinch of salt. Brush the mixture over the top.
Bake for 55–60 minutes, or until the crust is golden and fully baked.
Remove from the oven and let cool slightly before slicing and serving.