In a large bowl, mix the all-purpose flour and salt. Add the vegetable oil and rub it into the flour until the mixture resembles coarse crumbs. Gradually add water, a little at a time, mixing until a smooth dough forms. Cover with a damp cloth and let it rest for 30 minutes.
While the dough is resting, boil the cubed potatoes in salted water until tender, about 10-15 minutes. Drain and mash the potatoes in a bowl.
In a skillet, heat a tablespoon of oil over medium heat. Add cumin seeds and let them sizzle for a few seconds. Add the green peas and sauté for 2-3 minutes.
Add the mashed potatoes to the skillet along with garam masala, coriander powder, turmeric powder, red chili powder, and salt. Mix well and cook for another 2-3 minutes. Remove from heat and let the filling cool.
Divide the dough into 8 equal portions. Roll each portion into a ball and then flatten it into an oval shape. Cut the oval in half to create two semi-circles.
Take one semi-circle and form a cone by folding it along the straight edge, sealing the edge with a little water. Fill the cone with the potato filling and seal the open edge by pressing it together with your fingers. Repeat with the remaining dough and filling.
Heat oil in a deep frying pan over medium heat. Once hot, carefully add the samosas in batches, frying until golden brown and crispy, about 5-7 minutes. Drain on paper towels.
Serve hot with mint chutney or tamarind sauce.