For the chutney: In a food processor combine the mango, paprika and cardamom. Pulse until slightly chunky. Add the basil and mint, and pulse until herbs are chopped. Transfer to a bowl or resealable container and store in the fridge until ready to serve with the samosas.
For the dough: In large bowl combine the flour, paprika, salt and turmeric, and mix with a fork. Add the oil and 3/4 cup water and mix until a dough forms in the bowl. It should have a consistency similar to bread dough. Mix in a little more water if the dough is dry and stiff. Transfer to a floured counter and knead with your hands until smooth, 2 to 3 minutes. Cover the dough and set aside to rest while you prepare filling.
For the filling: Add the sweet potatoes and yams to a pot of salted water. Bring to a boil and cook until tender, about 8 minutes. Strain and let cool to room temp. You can rinse with cold water to speed up the cooling process.
In a large bowl combine the boiled potatoes and yams, the peas, cumin, cardamom and season with salt. Mix with a fork and set aside.
To make the samosas, portion off a golf-ball-size piece of dough and roll it into a ball. Dust your working surface with flour so the dough doesn't stick. Using a rolling pin, roll the dough ball into a thin round, a little thicker than a tortilla. Cut the circle in half. Take one of the half circles and make a cone shape by taking the two ends of the cut side and folding them into the center of the curve, so that the center of the cut side makes the point of the cone. Then wet the edges with a little water to glue the seam, and pinch together to seal.
Place a heaping tablespoon of filling into the cone, moisten the top of the edges and close the cone, pressing the edges to seal it. Repeat the process with the remaining dough and filling.
Add enough cooking oil to a medium-size heavy saucepan so the samosas won't touch the bottom. Heat the oil on medium-low heat to 350 degrees F. Working in batches of 4, carefully add the samosas to the oil and fry until both sides are golden brown, 4 to 6 minutes. Drain on a sheet pan lined with paper towels.
Serve warm with the fresh mango chutney.