In a large mixing bowl combine flour, instant or active dry yeast, sugar, and salt — add water gradually while mixing until a soft slightly sticky dough forms that is pliable and smooth not stiff or crumbly.
Knead dough for 8–10 minutes until smooth elastic and springs back when poked.
Coat dough ball lightly in neutral oil cover bowl with plastic wrap or clean kitchen towel and leave in a warm spot for exactly 1 hour until dough is noticeably puffier and lighter — do not rush this step.
While dough rests prepare potato patty mixture — in a large bowl combine boiled mashed potatoes with finely chopped mixed vegetables, chopped green chilies, dried oregano, red chili flakes, and chaat masala — do not add salt.
Add 1½ cups breadcrumbs and roughly chopped fresh cilantro to the potato mixture and mix thoroughly until completely combined and mixture holds together firmly when pressed.
If mixture feels too wet to shape add a small additional amount of breadcrumbs until mixture holds its shape cleanly.
Shape potato mixture into round flat patties slightly larger than the planned bun diameter — set aside.
In a shallow bowl whisk together all-purpose flour and water until a smooth slightly thick batter forms — consistency should coat the back of a spoon without running off immediately.
Dip each shaped potato patty into the flour batter making sure every surface is evenly and completely coated.
Immediately press each battered patty firmly into breadcrumbs turning and pressing gently to make sure breadcrumb coating covers every surface completely and evenly.
Heat a generous amount of neutral oil in a deep skillet over high heat until shimmering hot.
Add coated patties and fry for 3–4 minutes per side until deeply golden brown and audibly crispy all over — do not fry on lower heat as this produces pale soft coating rather than the crispy shell required.
Remove fried patties and drain on paper towel-lined plate — set aside.
Preheat oven to 350°F (180°C).
After the full 1-hour dough rest divide risen dough into equal portions — one per burger.
Roll or press each portion into a thick round flatbread — make it thick not thin as thickness gives the bun its substantial satisfying quality after baking.
Place flattened dough round on clean surface and stack chosen fillings in the center in this order — tandoori mayo, cheese slice, crispy potato patty, cheese sauce, chipotle sauce, potato slices, eggplant, tomato, cucumber, mustard sauce, sliced onion, and any additional chosen vegetables.
Gather edges of dough up and over the filling pulling them together at the top and twisting or pinching firmly to seal completely — similar to sealing a dumpling or filled bread roll — make sure the seal is tight with no gaps as any opening will cause bun to burst during baking.
Place sealed filled buns on a parchment-lined baking sheet.
Brush exterior of each bun generously with melted unsalted butter coating every visible surface evenly — butter coverage directly impacts final color and flavor.
Sprinkle white sesame seeds generously over the top surface of each bun.
Bake on center rack at 350°F for 20–25 minutes until bun is golden brown all over fully cooked through and sesame seeds are lightly toasted.
Remove from oven and allow to cool for 5 minutes before serving — interior will be very hot immediately after baking.
Serve warm and eat by hand.