Place the potatoes in a saucepan, add salt, and cover with cold water. Bring to a boil, then reduce the heat and simmer until fork-tender, about 15 minutes.

Drain the potatoes well and transfer them to a large mixing bowl. Mash the potatoes until smooth and set aside to cool slightly.

Heat the oil in a large pan over medium-high heat until it shimmers. Add the urad dal and cook until it starts to turn light brown, then add the mustard seeds and cook until they begin to pop.

Reduce the heat to medium and stir in the curry leaves and asafetida. Add the onion and a pinch of salt, and continue to cook until softened and starting to brown, about 10 minutes.

Stir in the green chili and ginger and cook until fragrant. Add the carrots and continue to cook until tender, about 3 minutes more.

Stir in the coriander, cumin, and turmeric, then remove the pan from the heat. Mix in the lime juice and adjust the salt to taste. Allow the filling to cool completely—a warm filling will steam and tear the delicate phyllo dough.

Preheat the oven to 375°F and grease a 9x13-inch baking dish. Divide the cooled potato filling into six equal portions.

Lay one sheet of phyllo on a clean work surface, keeping the remaining stack covered with a damp kitchen towel to prevent drying. Brush or spray a thin layer of oil evenly over the sheet, then layer a second sheet on top. Repeat once more with a third sheet and a final brush of oil.

Arrange one portion of the filling into an even log along the shorter end of the phyllo stack, about 1 inch from the edge. Roll the dough tightly around the filling and place the roll into the prepared baking dish.

Repeat the layering and rolling process for the remaining portions until you have six rolls. Place them side by side in the dish, brush the tops with a final layer of oil, and sprinkle with sesame seeds.

Bake on the upper rack of the oven until the tops are evenly golden brown and crisp, 45 to 55 minutes.

Allow the rolls to cool for 5 minutes, then cut into desired lengths with a sharp knife. Serve immediately while the pastry is still hot and crackling.