Prepare sourdough: Mix milk, flour, and yeast in a bowl and let it rest for 20 minutes.
Make Tang Zhong: In a saucepan, heat milk and flour until thickened, then let cool.
Combine mixtures: Add the cooled Tang Zhong to the sourdough and mix.
Add remaining ingredients: Add flour, sugar, eggs, zest, cardamom, mahlepi, mastic, vanilla, and salt. Mix well.
Incorporate butter: Add cubed butter and mix until smooth and elastic.
Let rise: Transfer dough to an oiled bowl, cover, and let rise for 1 hour.
Shape the buns: Divide dough, shape into buns, and place on a baking sheet.
Second rise: Cover and let rise again for 1 hour.
Bake: Bake in a preheated oven at 160°C for 30 minutes.
Glaze and serve: Brush with melted butter and serve.