Prepare Filling - Sear Beef: In a frying pan, heat 1 tbsp cooking oil. Add beef and sear on medium flame from all sides until golden. Set aside.
Cook Aromatics and Spices: In the same pan, add chopped onion and ginger garlic paste. Mix well and cook for 1 minute. Add Himalayan pink salt, black pepper powder, paprika powder, and cumin powder. Mix well.
Combine Beef and Simmer: Add 1-2 tbsp water and mix. Return seared beef to the pan, add 1 cup water, mix, and bring to a boil. Cover and cook on low flame until beef is tender, about 1 1/2 hours.
Shred Beef and Add Sauces: Turn off flame. Shred beef using forks and mix well. Turn on flame again, add BBQ sauce and hot sauce, mix well, cook for 1 minute, then set aside.
Prepare Dough - Activate Yeast: In a bowl, combine instant yeast, caster sugar, and 1/4 cup warm water. Mix well, cover, and let it bloom for 10-12 minutes.
Make Dough: Add egg, yogurt, and 1 tbsp cooking oil to the yeast mixture and whisk well. Add sifted all-purpose flour, Himalayan pink salt, and baking powder. Mix well. Gradually add about 1 cup water and knead until a dough forms.
Proof Dough: Grease dough with cooking oil, cover, and let it proof for 1 1/2 hours.
Shape and Fill Buns: Sprinkle dry flour and knead dough until smooth. Divide dough into 60 g portions. Roll each into a ball and flatten with a rolling pin to about 4 inches diameter, thin at corners and thicker at center. Place 1 tbsp prepared filling and some grated cheddar and mozzarella cheese in the center. Gather edges, pinch and seal to form a ball.
Second Proof: Place stuffed buns on a greased and baking paper-lined tray. Cover with kitchen towel and let proof for 15 minutes.
Apply Egg Wash and Bake: Whisk egg yolk and milk in a bowl. Brush over buns and sprinkle sesame seeds. Bake in preheated oven at 200°C (392°F) for 15-20 minutes using both top and bottom grills.
Finish and Serve: After baking, brush buns with melted butter. Serve warm with tomato ketchup.