Samosas aren't difficult to make, although they do take a bit of time. The hardst part is trying to describe how to form them from a half-circle of dough to a filled cone.
If you have a tortilla press, use it to press out the circles of dough - it's easier and faster than rolling it out.
For vegan samosas, use vegetable shortening instead of ghee, choose vegetarian chutneys, and don't serve a raita.
Put the unpeeled potatoes in one layer in a pot, add cool water to cover them, then mix in two teaspoons of salt. Place over a medium flame and bring to the boil. Lower the heat and simmer until the potatoes are tender but not mushy. Drain them and, when the potatoes are cool enough to handle, strip off the skin. Cut the potatoes into small dice.
Fill the pot halfway with water (no need to wash it) and bring it to the boil. Add the peas and cook for one minute, then drain.
Cut the banana chilli in half lengthwise and scrape out the seeds. Finely mince the chilli. Mince the onion and cut the carrot into small dice.
Heat 30ml (2 tbsp) of oil in a large skillet (or wok) and when it's hot, add the mustard seeds, cumin seeds and curry leaves. Stir constantly until the mustard seeds start to pop, then add the onion, carrot and a sprinkling of salt. Turn the heat to low and cook until the onion is soft. Add the banana chilli, ginger, garam masala and chilli powder and stir constantly for about 30 seconds. Add the potato then season to taste with salt and mix thoroughly. Cook, stirring frequently, until the mixture is hot. Pull out and discard the curry leaves, then use a potato masher to roughly mash the mixture. Stir in the peas. While the mixture cools to room temperature, make the dough.
Melt the ghee then cool it to tepid. Thoroughly combine the flour and salt, then mix in the ghee and 75ml (1/4 cup and 1 tbsp) of ice water. Mix to form a rough dough; if it seems dry, add more ice water, a little at a time. Knead the dough until it's smooth and pliable. Wrap it in cling-film and leave at room temperature for 30 minutes.
Have a small bowl of water ready. On a very lightly floured work surface, roll the dough into a snake and cut it into 16 evenly sized pieces. Shape each piece into a ball and cover them with cling-film. Working with one piece of dough at a time, roll (or press) it into a 15cm (6in) circle, then cut it in half. Make the dough into a cone shape by joining the cut edges so they're slightly overlapping. Press the edges of the dough together so they adhere (if needed, very lightly dampen the cut edge to make it sticky). Make a circle with the fingers of your non-dominant hand and put the cone - pointed side down - in the circle. Spoon the filling into the cone to fill it tightly, leaving space at the top to seal the samosa. Very lightly brush the edges of the dough with water then fold them down over the filling and press tightly to seal. Place the filled samosa pointed side up on a tray lined with foil or parchment paper. Repeat the process with the remaining dough and filling. You should have about 32.
Pour oil into a wide pan to the depth of about 5cm (2in). Heat the oil to 180°C (350°F) then fry the samosas in batches. Fry them until they're medium brown, turning over as needed. Drain them on paper towels, then serve with chutney and/or raita.