In a large bowl, combine the warm milk, warm water, sugar, and instant yeast. Let sit for 5 minutes.
Add the vegetable oil, egg white, and salt. Mix well.
Gradually add the flour while mixing until a soft dough forms.
Knead for 8–10 minutes until smooth and elastic.
Cover and let the dough rise in a warm place until doubled in size, about 1 hour.
Meanwhile, heat olive oil in a skillet and cook the minced meat until browned.
Add the diced peppers, tomatoes, and tomato paste. Cook for 5–7 minutes.
Season with salt, black pepper, cumin, and pul biber. Remove from heat and allow to cool slightly.
Preheat the oven to 180°C (350°F).
Divide the dough into equal portions and roll each into an oval shape.
Transfer the dough to a lined baking tray and slightly fold the edges inward.
Spread the minced meat filling evenly over each pide.
Brush the dough edges with the reserved egg yolk.
Sprinkle grated kashar cheese over the filling.
Bake for 20–25 minutes or until golden brown and the cheese is melted.
Serve warm and enjoy.