Boil the diced potatoes in salted water until tender, about 8-10 minutes. Drain and mash lightly.
In a non-stick pan, heat 1 tablespoon vegetable oil over medium heat. Add cumin seeds and let them splutter.
Add chopped onions, green chilies, and grated ginger. Sauté until onions turn translucent.
Add diced carrots and cook for 3-4 minutes until slightly soft.
Add green peas and cook for another 2 minutes.
Add turmeric powder, red chili powder, coriander powder, garam masala, amchur, and salt. Stir well to combine.
Add the boiled mashed potatoes and chopped cilantro. Mix everything thoroughly and cook for 2 minutes. Remove from heat and add lemon juice. Let the filling cool completely.
Take one spring roll pastry sheet and cut it into two equal strips lengthwise.
Fold one strip into a cone shape, sealing the edge with a little water.
Fill the cone with 2 tablespoons of the vegetable filling.
Seal the open edge by folding and pressing firmly with water to form a triangular samosa shape.
Repeat the process with remaining pastry strips and filling.
Preheat the air fryer to 375°F (190°C) for 3 minutes.
Lightly spray each samosa with oil on all sides.
Place samosas in the air fryer basket in a single layer without overlapping.
Air fry for 12-15 minutes, turning halfway through, until golden brown and crispy.
Remove samosas from the air fryer and let them cool for 2 minutes before serving.