Heat 2 Tbsp of the oil in a frying pan on medium-high heat. Add the cumin seeds and let them toast and crackle for 15 seconds. Add the onion and sauté until it has softened, 3 to 4 minutes. Add the potato and carrot to the pan, and sauté for 2 to 3 minutes. Add ¼ cup of the water, season with salt to taste, stir, and cover with a lid. Cook for 5 minutes. Most of the water should be absorbed by the vegetables at this point.

Remove the lid from the pan and add the frozen peas. Cook for 1 minute, until the peas have warmed through. Remove the pan from the heat and stir in the fresh coriander. Allow the mixture to cool for 10 minutes.

Place the flour and the remaining ¼ cup water in a small bowl and mix to form a thick paste.

Cut the stack of thawed spring roll wrapper sheets into 3 even rectangles, about 3¼ × 10 inches (8 × 25 cm) each. From 1 rectangle, peel away 2 sheets together to form the pastry for the samosa. Store the remaining sheets under a damp cloth to prevent them from drying out.

Lay the pastry horizontally on a clean surface. Fold the pastry down the middle vertically to create a crease in the center. Open the pastry back up and take 1 corner of the pastry rectangle and bring it toward the crease, forming a triangle. The edge of the pastry should align with the crease. Spread the flour paste along the edge of the pastry that forms the triangle, then fold over the other corner of the pastry to form a cone.

Add 1 to 2 Tbsp of the filling to the cone. Fold over the remaining pastry to create a triangle, and seal the edges with the flour paste. Repeat with the remaining filling and samosa wrappers.

In a deep frying pan or wok, heat 3 inches (8 cm) of oil to 350°F. Fry the samosas in batches for 4 to 5 minutes, gently flipping once or twice during frying, until crispy and golden.

Drain on a paper towel. Serve hot with both chutneys.