In a bowl, mix the whole wheat flour, white flour, baking powder, and salt.
In another bowl, whisk the milk, egg, and olive oil.
Add the liquid mixture to the flour mixture and knead until you have a firm dough.
In a pan, heat a little oil and sauté the onion, peppers, and carrot until they soften.
Add the shredded chicken and spices, and stir well.
Roll out the dough on a floured surface.
Place the chicken filling in the middle and fold the dough over it as you like.
Brush the top of the pie with the beaten egg yolk and sprinkle with the shredded cheese.
Place the pie on a greased or parchment-lined baking tray. Bake in a preheated oven at 180°C (350°F) for 20-25 minutes, or until golden brown.
Serve the pie hot.