Boil the potatoes until tender, then peel and mash them in a large bowl. Mix in cilantro, green chili, cumin, garam masala, red chili powder, black pepper, amchur, chaat masala, and salt.
Divide the seasoned potato mixture into 10 portions and shape each one into a compact oval or log.
Remove the crusts from the bread slices. Quickly dip one slice in water, then gently press it between your palms to remove excess moisture.
Place a portion of the potato filling in the center of the softened bread. Roll the bread tightly around the filling and press the edges together to seal. Repeat with the remaining bread and filling.
Heat oil in a deep skillet or kadai over medium heat. Test the oil by dropping in a small piece of bread it should sizzle and rise gently.
Carefully fry the bread rolls in batches, turning occasionally, until golden brown and crisp on all sides. Avoid overcrowding the pan.
Remove the rolls with a slotted spoon and drain on paper towels. Serve hot with green chutney, tamarind chutney, or tomato ketchup.