In a large mixing bowl, combine warm water, warm milk, sugar, and yeast. Let sit for 5–10 minutes until slightly foamy.
Add softened butter and salt. Gradually add the flour while mixing until a soft dough forms.
Knead for 8–10 minutes until smooth and elastic.
Cover the bowl and let the dough rise in a warm place for about 45 minutes or until doubled in size.
Gently deflate the dough and divide it into 12 equal portions.
Roll each portion into a circle slightly larger than a tea saucer.
Place some cheese filling in the center of each dough circle.
Fold and shape the dough into traditional Böğçe parcels. Trim the top edges with kitchen scissors if desired.
Place the pastries on a parchment-lined baking tray and let them rest for 10–15 minutes.
Mix the egg yolk with 1 tablespoon milk and brush over the pastries.
Sprinkle with sesame seeds.
Bake in a preheated oven at 180°C (356°F) for 20–30 minutes until golden brown.
Remove from the oven and cover with a clean kitchen towel for a few minutes to keep them soft.
Serve warm or at room temperature.